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Home › Mathematics › HCF and LCM

HCF and LCM — Mathematics Questions & Practice

Practise 275 HCF and LCM questions from Mathematics for competitive exams such as UPSC, Banking, SSC and Railway. Read the worked questions below, check every answer with an explanation, and track what you get wrong.

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Practice questions on HCF and LCM — with answers

Try each question first, then open the answer. Explanations are included.

1. What is the LCM of 12 and 18?

  1. A24
  2. B36
  3. C48
  4. D72
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Answer: B

LCM of 12 and 18: 12=2²×3, 18=2×3². LCM = 2²×3² = 36.

2. Find the HCF of 24, 36 and 60.

  1. A6
  2. B10
  3. C12
  4. D18
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Answer: C

24=2³×3, 36=2²×3², 60=2²×3×5. Common factors: 2²×3=12.

3. Find the LCM of 15, 20 and 30.

  1. A60
  2. B90
  3. C120
  4. D180
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Answer: A

15=3×5, 20=2²×5, 30=2×3×5. LCM = 2²×3×5=60.

4. The HCF of two numbers is 12 and their LCM is 240. If one number is 48, what is the other?

  1. A50
  2. B55
  3. C60
  4. D65
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Answer: C

Product of two numbers = HCF × LCM = 12×240=2880. Other number = 2880/48=60.

5. Find the greatest number that divides 245 and 1029 leaving remainder 5 in each case.

  1. A8
  2. B12
  3. C16
  4. D20
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Answer: C

Subtract remainder: 245-5=240, 1029-5=1024. HCF(240,1024)=16.

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