HCF & LCM

Ladakh Police Sub-Inspector · Mathematics · 79 practice questions with answers and explanations: 36 Easy, 42 Medium, 1 Hard.

Sample questions

Sample Easy question 1

What is the LCM of 18 and 14?

  1. 127
  2. 252
  3. 2
  4. 126
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Answer: D. LCM(18, 14) = 126.

Sample Easy question 2

What is the LCM of 18, 24 and 8?

  1. 3456
  2. 144
  3. 90
  4. 72
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Answer: D. LCM(18, 24, 8) = 72.

Sample Easy question 3

What is the HCF of 10, 8 and 12?

  1. 3
  2. 120
  3. 4
  4. 2
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Answer: D. HCF(10, 8, 12) = 2.

Sample Medium question 4

Find the smallest number that is exactly divisible by 6, 8 and 12.

  1. 48
  2. 24
  3. 12
  4. 72
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Answer: B. LCM(6, 8, 12): 6 = 2×3, 8 = 2³, 12 = 2²×3 → 2³×3 = 24.

Sample Medium question 5

The HCF of two numbers is 8 and their LCM is 48. If one number is 16, find the other.

  1. 24
  2. 12
  3. 48
  4. 32
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Answer: A. The product of the numbers is 8 × 48 = 384, so the other number = 384 ÷ 16 = 24.

Sample Medium question 6

Three bells ring at intervals of 10, 15 and 20 minutes. They ring together at 9:00 a.m. At what time will they next ring together?

  1. 9:30 a.m.
  2. 9:45 a.m.
  3. 11:00 a.m.
  4. 10:00 a.m.
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Answer: D. LCM(10, 15, 20) = 60 minutes, so they ring together again an hour later, at 10:00 a.m.

Sample Hard question 7

Find the HCF of the fractions 2/3, 4/9 and 8/27.

  1. 4/9
  2. 2/27
  3. 8/27
  4. 2/3
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Answer: B. HCF of fractions = HCF of numerators ÷ LCM of denominators = HCF(2, 4, 8) ÷ LCM(3, 9, 27) = 2/27.

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