HCF & LCM

JKSSB Assistant Training Officer (Handicrafts & Handlooms) · Numerical Ability · 79 practice questions with answers and explanations: 36 Easy, 42 Medium, 1 Hard.

Sample questions

Sample Easy question 1

What is the HCF of 18, 6 and 21?

  1. 6
  2. 4
  3. 126
  4. 3
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Answer: D. HCF(18, 6, 21) = 3.

Sample Easy question 2

Three bells ring together at 8:00 a.m. and then ring at intervals of 9, 8 and 12 minutes. After how many minutes will they next ring together?

  1. 29
  2. 144
  3. 36
  4. 72
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Answer: D. The next common ring is after LCM(9, 8, 12) = 72 minutes.

Sample Easy question 3

Three bells ring together at 8:00 a.m. and then ring at intervals of 30, 12 and 9 minutes. After how many minutes will they next ring together?

  1. 180
  2. 51
  3. 360
  4. 90
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Answer: A. The next common ring is after LCM(30, 12, 9) = 180 minutes.

Sample Medium question 4

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 Medium question 5

The HCF of two numbers is 6 and their LCM is 378. If one number is 42, what is the other?

  1. 54
  2. 420
  3. 60
  4. 336
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Answer: A. Product of the numbers = HCF × LCM, so other = 6×378/42 = 54.

Sample Medium question 6

The HCF of two numbers is 12 and their LCM is 24. What is the product of the two numbers?

  1. 288
  2. 300
  3. 48
  4. 36
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Answer: A. Product = HCF × LCM = 12 × 24 = 288.

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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