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HCF and LCM questions and answers

The highest common factor (HCF) is the biggest number that divides into both numbers. The lowest common multiple (LCM) is the smallest number both divide into. For bigger numbers, use prime factors: the HCF uses the primes they share (lowest powers), the LCM uses every prime (highest powers).

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated .

Start the questions How to find the HCF How to find the LCM guide HCF calculator

Where hcf and lcm comes up

GCSE (AQA, Edexcel, OCR)Foundation and Higher: use the concepts of factors, multiples, highest common factor and lowest common multiple, including from prime factorisations.
Cambridge IGCSE (0580)Core and Extended: identify and use common factors, common multiples, the HCF and the LCM.

The method

  1. Small numbers: list factors (for the HCF) or multiples (for the LCM).
  2. With prime factors: HCF = product of shared primes with the lowest powers.
  3. LCM = product of all primes with the highest powers.
  4. "When do they next meet?" is an LCM question; "biggest equal pieces" is an HCF question.

HCF and LCM questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Find the HCF of 12 and 18.

Question 2Warm-upFoundation

Find the LCM of 4 and 6.

Exam-style

Question 3Exam-styleFoundation

Find the HCF of 24 and 36.

Question 4Exam-styleFoundation

Find the LCM of 8 and 12.

Question 5Exam-styleFoundation

A=23×3A = 2^3 \times 3 and B=22×32×5B = 2^2 \times 3^2 \times 5. Find the HCF and the LCM of A and B.

Question 6Exam-styleFoundation

One bus leaves every 12 minutes and another every 15 minutes. Both leave at 9:00. How many minutes until they next leave together?

Challenge

Question 7ChallengeFoundation

Find the HCF of 84 and 120.

Question 8ChallengeFoundation

A floor is 240 cm by 180 cm. What is the largest square tile that fits exactly, with no cutting?

Common mistakes

  • Mixing up HCF and LCM.
  • Multiplying the two numbers to get the LCM (that's only sometimes right).
  • Using the highest powers for the HCF.

Stuck on one of these?

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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