HCF & LCM: GCSE Questions

Videos, examples and solutions to help GCSE Maths students learn how to find the highest common factor (HCF) and lowest common multiple (LCM).

The following diagram shows how use Repeated Division to find the HCF and LCM.

 

How to work with HCF and LCM?
Exam questions
Examples:

1. Write 140 as a product of its prime factors.
2. Write 720 as a product of its prime factors.
3. (a) Express the following as a product of its prime factors.
   (i) 60
   (ii) 96
   (b) Find the highest common factor of 60 and 96.
   (c) Find the lowest common multiple of 60 and 96.
4. (a) Express 120 as the product of powers of its prime factors.
   (b) Find the lowest common multiple of 120 and 150.
5. (a) Express 108 as the product of powers of its prime factors.
   (b) Find the highest common factor (hcf) of 108 and 24.
6. (a) Find the highest common factor (hcf) of 24 and 64.
   (b) Find the lowest common multiple (lcm) of 24 and 64.
7. (a) Find the highest common factor (hcf) of 75 and 90.
   (b) Find the lowest common multiple (lcm) of 75 and 90.

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How to work out the Highest Common Factor and Lowest Common Multiple using factorisation and short division?
Using Prime factorisation for HCF and LCM (Recap) GCSE Maths revision help

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Product of primes to find HCF and LCM, GCSE Maths revision Exam paper practice

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Prime Factorisation and HCF, LCM GCSE Maths revision Exam paper practice & help

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How to work out HCF and LCM using short division
How to work out the Highest Common Factor and Lowest Common Multiple using short division. Useful for quick calculations where a factor tree isn’t required. GCSE level C.

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Examples from Edexcel IGCSE past papers on finding prime factorisations, HCF (highest common factor) and LCM (lowest common multiple)
Examples:

1. Express 225 as the product of powers of its prime factors.
2. Express 132 as the product of powers of its prime factors.
3. (a) Express 200 as the product of powers of its prime factors.
   (b) Work out the lowest common multiple of 75 and 200. 4.(a) Find the Highest Common Factor of 75 and 105.
   (b) Find the Lowest Common Multiple of 75 and 105. 5.(a) Find the Highest Common Factor of 64 and 80.
   (b) Find the Lowest Common Multiple of 64 and 80. 6.(a) Find the Highest Common Factor of 72 and 90.
   (b) Find the Lowest Common Multiple of 72 and 90.

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