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GCSE Maths: HCF & LCM

Find the highest common factor and lowest common multiple using prime factor trees. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

NumberFoundation & HigherAQA · Edexcel · OCR · Eduqas

What you need to know

The concepts examiners test on hcf & lcm, and what each one is really asking.

Find the HCF of two or more numbers
Find the LCM of two or more numbers
Use prime factor decomposition
Apply HCF and LCM to word problems

Where marks get lost

The exam technique that separates a correct method from a correct answer.

  • Confusing HCF and LCM
  • Not breaking down to prime factors fully
  • For LCM: forgetting to use the maximum count of each prime
  • For HCF: using all primes instead of only shared ones

HCF & LCM questions students ask

Is HCF & LCM on the Foundation paper?

Yes. HCF & LCM appears at both Foundation and Higher tier, though Higher papers take it further.

What should I know before starting HCF & LCM?

It builds on Factors, multiples, and primes and Prime factorisation and Times tables. If those feel shaky, practise them first — HCF & LCM questions assume them.

What is the most common mistake in HCF & LCM?

Confusing HCF and LCM.

Which exam boards cover HCF & LCM?

All four we support — AQA, Edexcel, OCR and Eduqas. GCSE Maths subject content is set by the DfE, so the topic is common to every board; what changes is the paper structure and the grade boundaries.