HCF & LCM

Ladakh Police Constable · 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, 8 and 12?

  1. 1728
  2. 90
  3. 72
  4. 144
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Answer: C. LCM(18, 8, 12) = 72.

Sample Easy question 2

What is the smallest positive number that is exactly divisible by 9, 3 and 4?

  1. 36
  2. 45
  3. 72
  4. 108
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Answer: A. It is LCM(9, 3, 4) = 36.

Sample Easy question 3

What is the HCF of 6 and 8?

  1. 4
  2. 2
  3. 3
  4. 24
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Answer: B. HCF(6, 8) = 2.

Sample Medium question 4

Two numbers are in the ratio 3 : 5 and their LCM is 225. Find their HCF.

  1. 25
  2. 5
  3. 15
  4. 9
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Answer: C. Let the numbers be 3k and 5k. Their LCM is 15k = 225, so k = 15, which is also the HCF.

Sample Medium question 5

What is the least number of square tiles needed to pave a rectangular floor 4.8 m long and 3.6 m wide, using the largest possible tile?

  1. 12
  2. 9
  3. 24
  4. 16
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Answer: A. Largest tile side = HCF(480, 360) = 120 cm. Tiles = (480 ÷ 120) × (360 ÷ 120) = 4 × 3 = 12.

Sample Medium question 6

Find the smallest 4-digit number that is exactly divisible by 12, 15 and 20.

  1. 1020
  2. 1000
  3. 1080
  4. 1200
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Answer: A. LCM(12, 15, 20) = 60. The smallest multiple of 60 that is at least 1,000 is 60 × 17 = 1,020.

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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