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This topic writes numbers as products of prime factors and uses them to find the highest common factor (HCF) and lowest common multiple (LCM) of two or more numbers. It's examined right across GCSE and iGCSE Maths. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Write both numbers as products of primes. For the highest common factor, multiply the primes they share, taking the lower power of each. For the lowest common multiple, multiply every prime that appears, taking the higher power. A Venn diagram of the prime factors makes both readable at a glance.
Before you start
Before starting, revisit prime factorisation. Foundation and Higher tier students all cover it. Keep it sharp for fraction work and problems about repeating events.
What you learn
Writing a number as a product of primes unlocks a reliable way to find the LCM and HCF of any two numbers — a guaranteed exam earner. The HCF is the biggest number that divides into both. The LCM is the smallest number both divide into. The course works through prime factorisation, highest Common Factor (HCF) and lowest Common Multiple (LCM). Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Primes & LCM / HCF as one of the Number topics in our GCSE course library, at Foundation tier. You work through 3 concepts and 2 worked examples, testing yourself at 3 points. Nearby topics in the same strand are Primes & Proof, Product Rule for Counting and Reverse Percentages. For unlimited practice, the Number revision engine builds new questions on demand and records your accuracy.
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