NumberFoundation and Higher

Factors and multiples: GCSE maths practice with worked answers

Show Working has 1 kind of factors and multiples question for GCSE Maths, for Foundation and Higher. Every question is new each time and comes with the working, step by step.

This topic covers the highest common factor (HCF) and the lowest common multiple (LCM) of two numbers. They come up on their own and inside other questions, such as simplifying fractions or working out when two events next happen together.

Coming soon to the App Store

Worked example 1: hcf and lcm

Find the highest common factor (HCF) of 48 and 36.

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
The biggest number in both lists is 12.

Answer 12

01 / What's covered1 kind of question

Factors and multiples questions in the app

Each kind makes fresh questions every time, so you can practise as often as you like.

HCF and LCMBoth tiers

Worked example 2: hcf and lcm

Find the lowest common multiple (LCM) of 18 and 45.

Multiples of 18: 18, 36, 54, 72, 90.
Multiples of 45: 45, 90.
The smallest number in both lists is 90.

Answer 90

A common mistake

Mixing up the two. The HCF is the biggest number that divides into both. The LCM is the smallest number both divide into, so it is never smaller than the larger number.

02 / Practise itiPhone and iPad

Practise factors and multiples in Show Working

In the app, open Topics and choose Factors and multiples for ten fresh questions. Ask for a hint if you are stuck, and open the working to see the method one step at a time.