1. Different Methods of Finding HCF and LCM
There is no single best method for every HCF-LCM question. Small numbers can often be handled mentally, prime factorisation works well when numbers factor easily, the ladder method is convenient for several numbers, and successive division is especially powerful for finding the HCF of two large integers.
Main Methods:
• Listing factors or multiples
• Prime factorisation
• Common division or ladder method
• Euclidean or successive division method for HCF
• HCF-LCM product relation for two numbers
Exam Tip:
Do not force the same method on every question. Selecting the right method is itself an important calculation shortcut.
Scope:
This topic deals with methods for positive integers. HCF and LCM of fractions, decimals and special forms will be studied separately in Topic 3.3.
2. Listing Factors and Multiples
For small numbers, HCF can be found by listing factors and LCM by listing multiples.
Example — HCF:
Find HCF of 12 and 18.
Factors of 12:
1, 2, 3, 4, 6, 12
Factors of 18:
1, 2, 3, 6, 9, 18
Common factors:
1, 2, 3, 6
HCF=6.
Example — LCM:
Find LCM of 4 and 6.
Multiples of 4:
4, 8, 12, 16, ...
Multiples of 6:
6, 12, 18, ...
First positive common multiple=12.
Best Use:
Use the listing method when the numbers are small and the answer is visible quickly.
Exam Trap:
Listing multiples of large numbers is usually slow. Switch to prime factorisation or another method instead.
3. Prime Factorisation Method
Prime factorisation is one of the most important methods for finding both HCF and LCM. Each number is expressed as a product of prime powers.
For HCF:
Take only the prime factors common to all the numbers, using their lowest powers.
For LCM:
Take every prime factor appearing in any of the numbers, using its highest power.
Example:
Find the HCF and LCM of 60 and 72.
60 = 22 × 3 × 5
72 = 23 × 32
For HCF, take lowest powers of common primes:
HCF = 22 × 3
=12.
For LCM, take highest powers of all primes:
LCM = 23 × 32 × 5
=360.
Memory Rule:
HCF → Common primes + Lowest powers
LCM → All primes + Highest powers
Common Mistake:
Do not take the highest powers while finding HCF or the lowest powers while finding LCM.
Example with Three Numbers:
Find HCF and LCM of 12, 18 and 30.
12=22×3
18=2×32
30=2×3×5
HCF=2×3=6.
LCM=22×32×5
=180.
4. Common Division or Ladder Method
The common division method is especially convenient when HCF or LCM of several numbers has to be calculated without writing separate prime factorisations.
For HCF:
Divide all the numbers simultaneously only by a factor common to every number. Continue while a common divisor greater than 1 exists. Multiply the common divisors used.
Example — HCF of 24, 36 and 60:
24, 36, 60 ÷2 → 12, 18, 30
12, 18, 30 ÷2 → 6, 9, 15
6, 9, 15 ÷3 → 2, 3, 5
No common divisor greater than 1 remains.
HCF=2×2×3=12.
For LCM:
At each stage, divide by a prime factor that divides at least one of the numbers. Numbers not divisible by that prime are carried forward unchanged. Continue until all numbers become 1.
Example — LCM of 12, 18 and 30:
12, 18, 30 ÷2 → 6, 9, 15
6, 9, 15 ÷2 → 3, 9, 15
3, 9, 15 ÷3 → 1, 3, 5
1, 3, 5 ÷3 → 1, 1, 5
1, 1, 5 ÷5 → 1, 1, 1
LCM=2×2×3×3×5
=180.
Important Difference:
For HCF, the divisor must divide all current numbers.
For LCM, the divisor may divide one or more current numbers, while the others are carried unchanged.
5. Euclidean or Successive Division Method for HCF
For two large integers, HCF can often be found most efficiently by successive division. The method repeatedly replaces the larger problem with a smaller remainder problem.
Procedure:
1. Divide the larger number by the smaller number.
2. Divide the previous divisor by the remainder.
3. Continue this process.
4. When the remainder becomes 0, the last non-zero divisor is the HCF.
Division Identity:
Dividend = Divisor × Quotient + Remainder
Example:
Find HCF of 867 and 255.
867 = 255×3 + 102
255 = 102×2 + 51
102 = 51×2 + 0
Therefore the last non-zero divisor is 51.
HCF=51.
Exam Shortcut:
The successive-division method is usually faster than full prime factorisation when two large numbers are given.
Common Mistake:
The HCF is the last non-zero divisor, not the final remainder 0.
6. Working Backwards from Division Quotients
Some Railway and SSC-type questions give the quotients obtained during successive division together with the last divisor. In such questions, reconstruct the original numbers by working backwards.
Reverse Rule:
Dividend = Divisor × Quotient + Remainder
Example:
Suppose the successive quotients are 1, 5 and 2, and the last divisor is 15.
Start from the final step:
15×2+0=30.
Move one step backward:
30×5+15=165.
Move one more step backward:
165×1+30=195.
Therefore the two original numbers are:
165 and 195.
Their HCF is 15.
Exam Tip:
When reconstructing numbers, the remainder from the next division step becomes part of the previous calculation. Do not simply multiply all the quotients.
7. HCF-LCM Product Relation as a Calculation Shortcut
For exactly two positive integers, the product relation can turn an HCF or LCM question into a single division.
Formula:
First Number × Second Number = HCF × LCM
Therefore:
LCM = (First Number × Second Number) ÷ HCF
HCF = (First Number × Second Number) ÷ LCM
Unknown Number = (HCF × LCM) ÷ Known Number
Example:
Numbers are 306 and 657 and their HCF is 9.
LCM
=(306×657)/9
=22338.
Verification Shortcut:
After calculating HCF and LCM of two numbers by another method, check whether:
HCF×LCM = product of the two numbers.
Important:
Do not directly use this two-number product formula for three or more numbers.
8. Stepwise HCF and LCM of Three or More Numbers
HCF and LCM can also be calculated progressively. This is particularly useful when numbers are added one at a time.
HCF Property:
HCF(a,b,c)=HCF(HCF(a,b),c)
LCM Property:
LCM(a,b,c)=LCM(LCM(a,b),c)
Example — HCF:
Find HCF of 48, 72 and 120.
HCF(48,72)=24.
Then:
HCF(24,120)=24.
Example — LCM:
Find LCM of 8, 12 and 18.
LCM(8,12)=24.
Then:
LCM(24,18)=72.
9. Extracting a Common Multiplier Before Calculation
If all numbers contain an obvious common factor, remove it first and work with smaller numbers.
Property:
HCF(ka,kb)=k×HCF(a,b)
LCM(ka,kb)=k×LCM(a,b)
Example:
Find HCF of 84 and 126.
84=42×2
126=42×3
Since 2 and 3 are co-prime:
HCF=42.
Example:
Find LCM of 24 and 40.
24=8×3
40=8×5
LCM=8×LCM(3,5)
=8×15
=120.
Shortcut:
Whenever all numbers visibly contain a large common factor, factor it out before doing longer calculations.
10. Choosing the Fastest Method
Use Listing when:
Numbers are very small and common factors or multiples are obvious.
Use Prime Factorisation when:
Numbers can be factorised easily or both HCF and LCM are required.
Use Ladder Method when:
Three or more numbers are involved, especially for LCM.
Use Successive Division when:
HCF of two relatively large numbers is required.
Use Product Relation when:
For two numbers, HCF/LCM and enough of the other values are already given.
Exam Strategy:
Always inspect the numbers before starting. A question that looks lengthy by one method may take only a few seconds by another.
11. Common Exam Traps
Trap 1:
Using highest prime powers for HCF instead of lowest common powers.
Trap 2:
For LCM, including only primes common to all numbers instead of every required prime.
Trap 3:
In the HCF ladder method, dividing only some of the numbers by a chosen common divisor.
Trap 4:
In the LCM ladder method, incorrectly dropping a number that is not divisible by the current prime. It must be carried forward unchanged.
Trap 5:
Taking the final remainder 0 as the HCF in successive division.
Trap 6:
Reconstructing numbers from division quotients without adding the appropriate remainder.
Trap 7:
Using HCF×LCM=product as a direct identity for three or more numbers.
Trap 8:
Doing lengthy prime factorisation when one number already divides the other exactly.
12. Quick Revision
Remember:
• Listing is best for very small numbers.
• Prime factorisation works for both HCF and LCM.
• HCF uses common primes with lowest powers.
• LCM uses all required primes with highest powers.
• In the HCF ladder method, divide all numbers together by a common factor.
• In the LCM ladder method, a prime may divide only some numbers; carry the others unchanged.
• In successive division, the last non-zero divisor is the HCF.
• Dividend = Divisor×Quotient + Remainder.
• Division data can be reconstructed by working backwards.
• For two numbers: HCF×LCM = product of numbers.
• HCF(a,b,c)=HCF(HCF(a,b),c).
• LCM(a,b,c)=LCM(LCM(a,b),c).
• Common multipliers can often be factored out first.
• Choose the method that gives the answer with minimum reliable calculation.
13. Verified Previous-Year Questions
RRB ALP PYQ
LCM by Prime Factorisation
20 August 2018 · Shift I
Q1. Find the LCM of 15, 18 and 24.
A. 3
B. 540
C. 6
D. 360
Correct Answer: D. 360
15=3×5
18=2×32
24=23×3.
Take the highest powers of all prime factors:
LCM=23×32×5
=8×9×5
=360.
RRC Group D PYQ
Prime Factorisation
5 November 2018 · Shift I
Q2. Find the HCF and LCM respectively of 60 and 72.
A. 16 and 360
B. 12 and 260
C. 12 and 360
D. 10 and 360
Correct Answer: C. 12 and 360
60=22×3×5
72=23×32.
HCF=22×3=12.
LCM=23×32×5=360.
RRB Group D PYQ
Successive Division
6 September 2022 · Shift III
Q3. While finding the HCF of two numbers by the division method, the successive quotients are 1, 5 and 2, and the last divisor is 15. What is the LCM of the two numbers?
A. 2145
B. 2130
C. 3045
D. 2115
Correct Answer: A. 2145
Work backwards.
15×2=30.
30×5+15=165.
165×1+30=195.
The numbers are 165 and 195 and HCF=15.
LCM
=(165×195)/15
=2145.
RRB NTPC PYQ
Reverse Euclidean Division
20 June 2025 · Graduate CBT-I · Shift I
Q4. While finding the HCF of two numbers by division, the successive quotients are 1, 4 and 6, and the last divisor is 29. Find their LCM.
A. 22470
B. 22480
C. 22476
D. 22475
Correct Answer: D. 22475
Work backwards from HCF=29.
29×6=174.
174×4+29=725.
725×1+174=899.
The numbers are 725 and 899.
LCM
=(725×899)/29
=725×31
=22475.
14. Practice MCQs
Practice MCQ
Q1. Find the HCF of 84 and 126.
A. 14
B. 21
C. 42
D. 63
Correct Answer: C. 42
84=2×42 and 126=3×42, while 2 and 3 are co-prime. Therefore HCF=42.
Practice MCQ
Q2. Find the LCM of 18, 24 and 30.
A. 180
B. 240
C. 360
D. 720
Correct Answer: C. 360
18=2×3², 24=2³×3 and 30=2×3×5. Highest powers give 2³×3²×5=360.
Practice MCQ
Q3. Find the HCF of 252 and 198 by successive division.
A. 9
B. 18
C. 27
D. 36
Correct Answer: B. 18
252=198×1+54; 198=54×3+36; 54=36×1+18; 36=18×2. Last non-zero divisor=18.
Practice MCQ
Q4. Find the LCM of 12, 15 and 20.
A. 40
B. 60
C. 120
D. 180
Correct Answer: B. 60
12=2²×3, 15=3×5 and 20=2²×5. Thus LCM=2²×3×5=60.
Practice MCQ
Q5. The product of two numbers is 4320 and their HCF is 12. Find their LCM.
A. 240
B. 300
C. 360
D. 420
Correct Answer: C. 360
LCM=4320÷12=360.
Practice MCQ
Q6. Find the HCF of 72, 120 and 168.
A. 12
B. 18
C. 24
D. 36
Correct Answer: C. 24
HCF(72,120)=24 and HCF(24,168)=24.
Practice MCQ
Q7. Find the LCM of 8, 12 and 18.
A. 36
B. 48
C. 72
D. 144
Correct Answer: C. 72
LCM(8,12)=24 and LCM(24,18)=72.
Practice MCQ
Q8. If HCF(144,180) is calculated by extracting their largest visible common factor, what is the HCF?
A. 18
B. 24
C. 36
D. 72
Correct Answer: C. 36
144=36×4 and 180=36×5. Since 4 and 5 are co-prime, HCF=36.
Practice MCQ
Q9. The HCF and LCM of two numbers are 12 and 480. If one number is 96, find the other.
A. 48
B. 60
C. 72
D. 80
Correct Answer: B. 60
Other number=(12×480)/96=60.
Practice MCQ
Q10. Using successive division, find the HCF of 867 and 255.
A. 17
B. 34
C. 51
D. 102
Correct Answer: C. 51
867=255×3+102; 255=102×2+51; 102=51×2. Hence HCF=51.
1. HCF एवं LCM ज्ञात करने की विभिन्न विधियाँ
हर HCF-LCM question के लिए एक ही method सबसे अच्छा नहीं होता। छोटे numbers को mentally solve किया जा सकता है, easily factor होने वाले numbers के लिए prime factorisation उपयोगी है, कई numbers के लिए ladder method convenient है और दो बड़े numbers का HCF निकालने के लिए successive division अत्यंत प्रभावी है।
मुख्य विधियाँ:
• Factors या multiples की listing
• Prime factorisation
• Common division या ladder method
• HCF के लिए Euclidean या successive division
• दो numbers के लिए HCF-LCM product relation
Exam Tip:
हर question पर एक ही method force न करें। सही method चुनना स्वयं एक महत्वपूर्ण calculation shortcut है।
Scope:
इस topic में positive integers के methods पढ़े जा रहे हैं। Fractions, decimals एवं special forms का HCF-LCM Topic 3.3 में पढ़ा जाएगा।
2. Factors एवं Multiples की Listing Method
Small numbers के लिए factors की list बनाकर HCF तथा multiples की list बनाकर LCM ज्ञात किया जा सकता है।
उदाहरण — HCF:
12 एवं18 का HCF ज्ञात करें।
12 के factors:
1, 2, 3, 4, 6, 12
18 के factors:
1, 2, 3, 6, 9, 18
Common factors:
1, 2, 3, 6
HCF=6।
उदाहरण — LCM:
4 एवं6 का LCM ज्ञात करें।
4 के multiples:
4, 8, 12, 16, ...
6 के multiples:
6, 12, 18, ...
पहला positive common multiple=12।
Best Use:
Listing method तब उपयोग करें जब numbers छोटे हों और answer जल्दी दिखाई दे।
Exam Trap:
Large numbers के multiples की लंबी list बनाने में समय न गँवाएँ। ऐसे questions में दूसरा method चुनें।
3. Prime Factorisation Method
Prime factorisation से HCF एवं LCM दोनों ज्ञात किए जा सकते हैं। प्रत्येक number को prime powers के product में लिखा जाता है।
HCF के लिए:
केवल सभी numbers में common prime factors लें और उनकी lowest powers चुनें।
LCM के लिए:
किसी भी number में आने वाले सभी आवश्यक prime factors लें और उनकी highest powers चुनें।
उदाहरण:
60 एवं72 का HCF और LCM ज्ञात करें।
60=22×3×5
72=23×32
HCF के लिए common primes की lowest powers:
HCF=22×3=12।
LCM के लिए सभी primes की highest powers:
LCM=23×32×5=360।
Memory Rule:
HCF → Common primes + Lowest powers
LCM → All required primes + Highest powers
Common Mistake:
HCF निकालते समय highest powers और LCM निकालते समय lowest powers न लें।
तीन Numbers का उदाहरण:
12, 18 एवं30 का HCF और LCM ज्ञात करें।
12=22×3
18=2×32
30=2×3×5
HCF=2×3=6।
LCM=22×32×5=180।
4. Common Division या Ladder Method
कई numbers का HCF या LCM निकालने में common division या ladder method बहुत उपयोगी होता है।
HCF के लिए:
सभी current numbers को केवल ऐसे common factor से simultaneously divide करें जो सभी numbers को divide करे। उपयोग किए गए सभी common divisors का product HCF होगा।
उदाहरण — 24, 36 एवं60 का HCF:
24,36,60 ÷2 → 12,18,30
12,18,30 ÷2 → 6,9,15
6,9,15 ÷3 → 2,3,5
अब कोई common divisor greater than1 नहीं है।
HCF=2×2×3=12।
LCM के लिए:
हर stage पर ऐसा prime factor चुनें जो कम-से-कम एक current number को divide करे। जो numbers उस prime से divide नहीं होते, उन्हें unchanged आगे ले जाएँ। सभी numbers 1 होने तक जारी रखें।
उदाहरण — 12, 18 एवं30 का LCM:
12,18,30 ÷2 → 6,9,15
6,9,15 ÷2 → 3,9,15
3,9,15 ÷3 → 1,3,5
1,3,5 ÷3 → 1,1,5
1,1,5 ÷5 → 1,1,1
LCM=2×2×3×3×5=180।
बहुत महत्वपूर्ण अंतर:
HCF में divisor को सभी current numbers को divide करना चाहिए।
LCM में divisor केवल एक या अधिक numbers को divide कर सकता है; बाकी numbers unchanged रहते हैं।
5. HCF के लिए Euclidean या Successive Division Method
दो बड़े integers का HCF successive division से बहुत तेजी से ज्ञात किया जा सकता है। प्रत्येक step में previous divisor और remainder का उपयोग किया जाता है।
Procedure:
1. Larger number को smaller number से divide करें।
2. Previous divisor को remainder से divide करें।
3. यही प्रक्रिया repeat करें।
4. Remainder 0 होने पर last non-zero divisor ही HCF है।
Division Identity:
Dividend = Divisor × Quotient + Remainder
उदाहरण:
867 एवं255 का HCF ज्ञात करें।
867=255×3+102
255=102×2+51
102=51×2+0
Last non-zero divisor=51।
HCF=51।
Exam Shortcut:
दो बड़े numbers का HCF निकालने में successive division अक्सर full prime factorisation से अधिक तेज होता है।
Common Mistake:
Final remainder 0 HCF नहीं है। उसके पहले वाला last non-zero divisor HCF होता है।
6. Division Quotients से Reverse Calculation
कुछ Railway एवं SSC-type questions में successive division के quotients और last divisor दिए जाते हैं। ऐसे questions में original numbers को reverse direction में reconstruct किया जाता है।
Reverse Rule:
Dividend = Divisor × Quotient + Remainder
उदाहरण:
Successive quotients 1, 5 और2 हैं तथा last divisor 15 है।
अंतिम step से शुरू करें:
15×2+0=30।
एक step पीछे:
30×5+15=165।
फिर:
165×1+30=195।
Original numbers:
165 और195।
इनका HCF=15।
Exam Tip:
Reverse calculation में केवल quotients का multiplication न करें। प्रत्येक stage पर सही remainder जोड़ना आवश्यक है।
7. HCF-LCM Product Relation का Shortcut
Exactly दो positive integers के लिए product relation कई questions को एक simple division में बदल देता है।
Formula:
पहली संख्या × दूसरी संख्या = HCF × LCM
इससे:
LCM=(पहली संख्या×दूसरी संख्या)/HCF
HCF=(पहली संख्या×दूसरी संख्या)/LCM
Unknown Number=(HCF×LCM)/Known Number
उदाहरण:
Numbers 306 एवं657 हैं और HCF=9 है।
LCM
=(306×657)/9
=22338।
Verification Shortcut:
दो numbers का HCF एवं LCM किसी अन्य method से निकालने के बाद check करें:
HCF×LCM = दोनों numbers का product।
Important:
इस two-number formula को तीन या अधिक numbers पर direct identity की तरह उपयोग न करें।
8. तीन या अधिक Numbers का Stepwise HCF-LCM
HCF Property:
HCF(a,b,c)=HCF(HCF(a,b),c)
LCM Property:
LCM(a,b,c)=LCM(LCM(a,b),c)
HCF Example:
48,72 एवं120 का HCF:
HCF(48,72)=24।
HCF(24,120)=24।
LCM Example:
8,12 एवं18 का LCM:
LCM(8,12)=24।
LCM(24,18)=72।
9. Calculation से पहले Common Multiplier निकालना
यदि सभी numbers में कोई बड़ा common factor स्पष्ट दिखाई दे रहा हो, तो उसे पहले बाहर निकालकर smaller numbers पर calculation करना आसान होता है।
Property:
HCF(ka,kb)=k×HCF(a,b)
LCM(ka,kb)=k×LCM(a,b)
उदाहरण:
84 एवं126 का HCF:
84=42×2
126=42×3
2 एवं3 co-prime हैं।
इसलिए HCF=42।
उदाहरण:
24 एवं40 का LCM:
24=8×3
40=8×5
LCM=8×LCM(3,5)
=8×15
=120।
Shortcut:
यदि सभी numbers में बड़ा common factor तुरंत दिखाई दे, तो longer calculation से पहले उसे factor out करें।
10. सबसे तेज Method कैसे चुनें?
Listing Method:
जब numbers बहुत छोटे हों।
Prime Factorisation:
जब numbers आसानी से factor हों या HCF और LCM दोनों चाहिए हों।
Ladder Method:
जब तीन या अधिक numbers हों, विशेषकर LCM के लिए।
Successive Division:
जब दो relatively large numbers का HCF चाहिए हो।
Product Relation:
जब exactly दो numbers के लिए HCF/LCM तथा पर्याप्त अन्य values पहले से दी गई हों।
Exam Strategy:
Calculation शुरू करने से पहले numbers को देखें। जो question एक method से लंबा दिखता है, वह दूसरे method से कुछ seconds में solve हो सकता है।
11. Common Exam Traps
Trap 1:
HCF में lowest common powers के स्थान पर highest powers लेना।
Trap 2:
LCM में केवल common primes लेना और बाकी prime factors छोड़ देना।
Trap 3:
HCF ladder method में चुने गए divisor से केवल कुछ numbers को divide करना।
Trap 4:
LCM ladder method में current prime से divisible न होने वाले number को हटाना। उसे unchanged आगे ले जाना चाहिए।
Trap 5:
Successive division में final remainder 0 को HCF मान लेना।
Trap 6:
Given quotients से numbers reconstruct करते समय appropriate remainder न जोड़ना।
Trap 7:
HCF×LCM=product formula को तीन या अधिक numbers पर directly apply करना।
Trap 8:
जब एक number दूसरे को exactly divide करती हो तब भी unnecessary lengthy factorisation करना।
12. Quick Revision
एक नज़र में:
• Small numbers के लिए listing useful है।
• Prime factorisation से HCF एवं LCM दोनों निकाले जा सकते हैं।
• HCF = common primes की lowest powers।
• LCM = सभी required primes की highest powers।
• HCF ladder में divisor सभी numbers को divide करेगा।
• LCM ladder में divisor कुछ numbers को divide कर सकता है; बाकी unchanged रहेंगे।
• Successive division में last non-zero divisor HCF है।
• Dividend=Divisor×Quotient+Remainder।
• Quotients से numbers reverse calculation द्वारा निकाले जा सकते हैं।
• Exactly दो numbers के लिए HCF×LCM=उनका product।
• HCF(a,b,c)=HCF(HCF(a,b),c)।
• LCM(a,b,c)=LCM(LCM(a,b),c)।
• Common multiplier को पहले factor out करना calculation आसान कर सकता है।
• हमेशा minimum reliable calculation वाला method चुनें।
13. Verified Previous-Year Questions
RRB ALP PYQ
LCM by Prime Factorisation
20 अगस्त 2018 · Shift I
प्रश्न 1. 15, 18 एवं24 का LCM ज्ञात करें।
A. 3
B. 540
C. 6
D. 360
सही उत्तर: D. 360
15=3×5
18=2×32
24=23×3।
सभी prime factors की highest powers लें:
LCM=23×32×5
=8×9×5
=360।
RRC Group D PYQ
Prime Factorisation
5 नवंबर 2018 · Shift I
प्रश्न 2. 60 एवं72 का क्रमशः HCF एवं LCM ज्ञात करें।
A. 16 एवं360
B. 12 एवं260
C. 12 एवं360
D. 10 एवं360
सही उत्तर: C. 12 एवं360
60=22×3×5
72=23×32।
HCF=22×3=12।
LCM=23×32×5=360।
RRB Group D PYQ
Successive Division
6 सितंबर 2022 · Shift III
प्रश्न 3. Division method से दो numbers का HCF ज्ञात करते समय successive quotients 1, 5 एवं2 प्राप्त होते हैं और last divisor 15 है। दोनों numbers का LCM क्या है?
A. 2145
B. 2130
C. 3045
D. 2115
सही उत्तर: A. 2145
Reverse calculation करें।
15×2=30।
30×5+15=165।
165×1+30=195।
Numbers 165 एवं195 हैं और HCF=15।
LCM
=(165×195)/15
=2145।
RRB NTPC PYQ
Reverse Euclidean Division
20 जून 2025 · Graduate CBT-I · Shift I
प्रश्न 4. दो numbers का HCF division method से निकालते समय successive quotients 1, 4 एवं6 हैं और last divisor 29 है। उनका LCM ज्ञात करें।
A. 22470
B. 22480
C. 22476
D. 22475
सही उत्तर: D. 22475
HCF=29 से reverse calculation करें।
29×6=174।
174×4+29=725।
725×1+174=899।
Numbers 725 एवं899 हैं।
LCM
=(725×899)/29
=725×31
=22475।
14. Practice MCQs
Practice MCQ
प्रश्न 1. 84 एवं126 का HCF ज्ञात करें।
A. 14
B. 21
C. 42
D. 63
सही उत्तर: C. 42
84=42×2 तथा126=42×3। 2 और3 co-prime हैं। इसलिए HCF=42।
Practice MCQ
प्रश्न 2. 18, 24 एवं30 का LCM ज्ञात करें।
A. 180
B. 240
C. 360
D. 720
सही उत्तर: C. 360
18=2×3², 24=2³×3 तथा30=2×3×5। Highest powers से LCM=2³×3²×5=360।
Practice MCQ
प्रश्न 3. Successive division से 252 एवं198 का HCF ज्ञात करें।
A. 9
B. 18
C. 27
D. 36
सही उत्तर: B. 18
252=198×1+54; 198=54×3+36; 54=36×1+18; 36=18×2। Last non-zero divisor=18।
Practice MCQ
प्रश्न 4. 12, 15 एवं20 का LCM ज्ञात करें।
A. 40
B. 60
C. 120
D. 180
सही उत्तर: B. 60
12=2²×3, 15=3×5 तथा20=2²×5। LCM=2²×3×5=60।
Practice MCQ
प्रश्न 5. दो numbers का product 4320 तथा HCF 12 है। उनका LCM ज्ञात करें।
A. 240
B. 300
C. 360
D. 420
सही उत्तर: C. 360
LCM=4320÷12=360।
Practice MCQ
प्रश्न 6. 72, 120 एवं168 का HCF ज्ञात करें।
A. 12
B. 18
C. 24
D. 36
सही उत्तर: C. 24
HCF(72,120)=24 तथाHCF(24,168)=24।
Practice MCQ
प्रश्न 7. 8, 12 एवं18 का LCM ज्ञात करें।
A. 36
B. 48
C. 72
D. 144
सही उत्तर: C. 72
LCM(8,12)=24 तथाLCM(24,18)=72।
Practice MCQ
प्रश्न 8. 144 एवं180 का HCF ज्ञात करें।
A. 18
B. 24
C. 36
D. 72
सही उत्तर: C. 36
144=36×4 तथा180=36×5। 4 और5 co-prime हैं। इसलिए HCF=36।
Practice MCQ
प्रश्न 9. दो numbers का HCF 12 तथा LCM 480 है। यदि एक number 96 है, तो दूसरी number ज्ञात करें।
A. 48
B. 60
C. 72
D. 80
सही उत्तर: B. 60
दूसरी number=(12×480)/96=60।
Practice MCQ
प्रश्न 10. Successive division द्वारा 867 एवं255 का HCF ज्ञात करें।
A. 17
B. 34
C. 51
D. 102
सही उत्तर: C. 51
867=255×3+102; 255=102×2+51; 102=51×2। इसलिए HCF=51।