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Lowest Common Multiple: GCSE Maths Definition

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Published

Read time

2 minutes

Contents

  1. 1. What is the lowest common multiple?
  2. 2. How can I find the lowest common multiple?
  3. 3. What is the lowest common multiple used for?
  4. 4. Lowest common multiple revision resources to ace your exams

What is the lowest common multiple?

In GCSE Maths, the lowest common multiple (LCM) is the smallest multiple that is shared by two or more numbers.

For example, the lowest common multiple of the numbers 4 and 6 is 24.

How can I find the lowest common multiple?

There is more than one way to find the lowest common multiple of two numbers.

Be careful, multiplying two numbers together will always result in a common multiple, but it won't necessarily be the lowest common multiple.

Listing multiples

You can find common multiples of two numbers by listing out the first few multiples of each number until the first multiple that is common to both occurs.

For example:

bold 8 colon space 8 comma space 16 comma space circle enclose 24 space space space space space space space space space space space space space bold space bold space bold 12 colon space 12 comma space circle enclose 24

The LCM of the numbers 8 and 12 is 24.

Prime factor decomposition

You can also use prime factor decomposition to find the LCM of two numbers.

Break down the numbers into their prime factors. You can then multiply together all prime factors that are common to both numbers and multiply the result by the remaining prime factors.

You may use the product of primes, a factor tree or a Venn diagram to help you with this.

For example:

Venn diagram showing the prime factors of the numbers 42 and 90. In the region of the diagram for 42 only, the only prime factor is 7. In the region of the diagram for 90 only, the prime factors are 3 and 5. In the region for both 42 and 90 are the prime factors 2 and 3.

The LCM of 42 and 90 is open parentheses 2 cross times 3 close parentheses cross times 7 cross times 3 cross times 5 equals 630

What is the lowest common multiple used for?

The lowest common multiple can be useful in a number of different situations when you need to find a shared value that two numbers both go into, including:

  • Finding a lowest common denominator and comparing two fractions

  • Working out the least number of packets you need to buy when you want the same number of two separate items, but the items come in packets of different quantities

  • Identifying when two events that occur at different regular intervals will next occur at the same time

Lowest common multiple revision resources to ace your exams

The lowest common multiple is covered in our revision notes on HCF & LCM from GCSE Maths. You can also have a go at our related exam questions and flashcards to test your understanding. Don’t forget to check out the past papers for more general exam revision.

Explore our GCSE Maths Revision Resources

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Author
Reviewer
Naomi C

Author: Naomi C

Expertise: Maths

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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