Quantitative Aptitude

HCF and LCM of Fractions: Practice Questions with Answers

14 practice questions on HCF and LCM of Fractions, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

Read the lesson on this topic →

1. Q.1

   Find the LCM of 4/5, 8/15, and 12/25, and verify it.

   Show answer

   Answer: 24/5

   Solution:

   1. LCM of numerators: LCM(4, 8, 12) = 24. HCF of denominators: HCF(5, 15, 25) = 5. LCM of fractions = 24/5.
   2. Verify: (24/5) ÷ (4/5) = 6 ✓, (24/5) ÷ (8/15) = 9 ✓, (24/5) ÷ (12/25) = 10 ✓ — all whole numbers, as required for a genuine LCM.

   Report this question

2. Q.2

   Find the LCM of 3/6 and 5/10.

   Show answer

   Answer: 1/2

   Solution:

   1. Reduce both first: 3/6 = 1/2 and 5/10 = 1/2 — they're actually the same value.
   2. LCM of numerators: LCM(1, 1) = 1. HCF of denominators: HCF(2, 2) = 2.
   3. LCM = 1/2 (the LCM of two equal values is just that value itself).

   Report this question

3. Q.3

   Find the HCF of 2/3 and 4/9.

   Show answer

   Answer: 2/9

   Solution:

   1. Both fractions are already in lowest terms.
   2. HCF of numerators: HCF(2, 4) = 2.
   3. LCM of denominators: LCM(3, 9) = 9.
   4. HCF of fractions = 2/9.

   Report this question

4. Q.4

   Find the HCF of 4/5, 8/15, and 12/25.

   Show answer

   Answer: 4/75

   Solution:

   1. All three fractions are already in lowest terms.
   2. HCF of numerators: HCF(4, 8, 12) = 4.
   3. LCM of denominators: LCM(5, 15, 25) = 75.
   4. HCF of fractions = 4/75.

   Report this question

5. Q.5

   Find the LCM of 2/3 and 4/9.

   Show answer

   Answer: 4/3

   Solution:

   1. Both fractions are already in lowest terms.
   2. LCM of numerators: LCM(2, 4) = 4.
   3. HCF of denominators: HCF(3, 9) = 3.
   4. LCM of fractions = 4/3.

   Report this question

6. Q.6

   Find the HCF of 6/7, 12/21, and 18/35 (notice 12/21 is not in lowest terms).

   Show answer

   Answer: 2/35

   Solution:

   1. Reduce 12/21 first: HCF(12,21) = 3, so 12/21 = 4/7. The other two fractions, 6/7 and 18/35, are already in lowest terms.
   2. Now apply the formula to 6/7, 4/7, 18/35: HCF of numerators = HCF(6, 4, 18) = 2. LCM of denominators = LCM(7, 7, 35) = 35.
   3. HCF of fractions = 2/35.

   Report this question

7. Q.7

   Find the HCF of 2/4 and 3/6.

   Show answer

   Answer: 1/2

   Solution:

   1. Neither fraction is in lowest terms: 2/4 = 1/2 and 3/6 = 1/2. Reduce both first.
   2. Now apply the formula to the reduced fractions: HCF(1, 1) = 1, LCM(2, 2) = 2. HCF = 1/2.
   3. Using the raw, unreduced numbers instead would have wrongly given HCF(2,3)/LCM(4,6) = 1/12 — this is why reducing first matters.

   Report this question

8. Q.8

   Find the HCF of 3/4 and 9/10.

   Show answer

   Answer: 3/20

   Report this question

9. Q.9

   Find the HCF of 4/8 and 6/12.

   Show answer

   Answer: 1/2. Both reduce to 1/2 first.

   Report this question

10. Q.10

    Find the LCM of 2/4 and 6/8.

    Show answer

    Answer: 3/2. Reduce first to 1/2 and 3/4; LCM(1,3)/HCF(2,4) = 3/2.

    Report this question

11. Q.11

    Find the HCF of 8/10, 4/5, and 12/20.

    Show answer

    Answer: 1/5. Reduce first to 4/5, 4/5, 3/5; HCF(4,4,3)/LCM(5,5,5) = 1/5.

    Report this question

12. Q.12

    Find the LCM of 5/6 and 7/9.

    Show answer

    Answer: 35/3. Both already in lowest terms: LCM(5,7)/HCF(6,9).

    Report this question

13. Q.13

    Find the LCM of 3/4 and 9/10.

    Show answer

    Answer: 9/2

    Report this question

14. Q.14

    Find the HCF of 6/7, 12/21, and 18/35.

    Show answer

    Answer: 2/35. Reduce 12/21 to 4/7 first (dividing by their HCF, 3); then HCF(6,4,18)/LCM(7,7,35).

    Report this question

Practise this topic →