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HCF and LCM of Fractions Solved Questions

This isn’t a new idea — it’s the same HCF/LCM method from whole numbers, applied to the numerators and denominators separately — but it only works correctly if you reduce every fraction to its lowest terms FIRST. This page covers the formula, that essential reduce-first step (with a worked example showing why skipping it can silently give a wrong answer), and a verification check, with several fully worked examples.

Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-05. Editorial standards & corrections

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The concept, quickly

  • HCF of fractions = HCF of the numerators / LCM of the denominators — provided every fraction has first been written in its lowest terms (numerator and denominator sharing no common factor).
  • LCM of fractions = LCM of the numerators / HCF of the denominators — under the same lowest-terms condition.
  • Always reduce every given fraction to lowest terms FIRST, before taking the HCF of the numerators or the LCM of the denominators. Skipping this can silently give a wrong answer: for 2/4 and 3/6 (both equal to 1/2), the raw unreduced formula gives HCF(2,3)/LCM(4,6) = 1/12 — which is NOT the correct HCF, since 1/2 itself is a far larger value that both fractions are exact multiples of. Reducing first (1/2 and 1/2) correctly gives HCF = 1/2.
  • Simplifying the FINAL answer (if it isn’t already in lowest terms) is a separate, optional last step for a cleaner answer — it does not substitute for reducing the inputs first, and won’t reliably fix an error introduced by skipping that step.
  • Check your answer: an HCF of fractions must divide evenly into every given fraction (each original ÷ your HCF should be a whole number); an LCM of fractions must itself be evenly divisible by every given fraction (your LCM ÷ each original should be a whole number).
  • The whole process mirrors whole-number HCF/LCM exactly — reduce each fraction, apply HCF/LCM to the numerators and denominators as described, then simplify the result if needed. The only new skill is handling a numerator and a denominator together instead of a single number.

Worked examples

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

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.

Answer: 2/9

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

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.

Answer: 4/3

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

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.

Answer: 4/75

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

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.

Answer: 24/5

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

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.

Answer: 1/2

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

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.

Answer: 2/35

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

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).

Answer: 1/2

Try these yourself

Reduce every fraction to lowest terms first, then apply the HCF/LCM formulas, and check against the answer.

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

Answer: 3/20

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

Answer: 9/2

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

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

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

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

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

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

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

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

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

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

All 14 practice questions on HCF and LCM of Fractions, with answers →

Where this comes up

HCF and LCM of Fractions is a regular sub-topic within the Quantitative/Numerical Aptitude section of exams Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — building directly on the standard LCM and HCF lesson.

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