Lowest Common Multiple
The lowest common multiple of two numbers is the smallest number that both of them divide into exactly.
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The lowest common multiple of two numbers is the smallest number that both of them divide into exactly.
- LCM of 4 and 6 is 12
- Use prime factors with the highest powers
- LCM is used to add fractions with different denominators
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Lowest Common Multiple?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Lowest Common Multiple. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Lowest Common Multiple in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Lowest Common Multiple gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Lowest Common Multiple in detail
The lowest common multiple (LCM) of two or more numbers is the smallest positive number that is a multiple of each of them. For 4 and 6 the multiples are 4, 8, 12 … and 6, 12, 18 …, so the LCM is 12. Prime factorisations give a faster method: take each prime to its highest power.
The LCM is the key to adding and subtracting fractions with different denominators and to solving timing problems, such as when two buses leaving a station at different intervals will next depart together. It is the partner idea to the highest common factor.
How the interactive helps you understand Lowest Common Multiple
Watch the Venn diagram in the interactive. Use any sliders or buttons it offers to change the values and see how the Venn diagram responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Lowest Common Multiple.
Real-life uses and examples
- Spot Lowest Common Multiple in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Lowest Common Multiple by estimating first, then working it out step by step.
- Use Lowest Common Multiple when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Lowest Common Multiple.
- Memorising the steps for Lowest Common Multiple without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Lowest Common Multiple
What is Lowest Common Multiple?
The lowest common multiple of two numbers is the smallest number that both of them divide into exactly.
What are the most important points about Lowest Common Multiple?
The main points are: LCM of 4 and 6 is 12; Use prime factors with the highest powers; LCM is used to add fractions with different denominators.
Why is Lowest Common Multiple useful?
Understanding Lowest Common Multiple gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Lowest Common Multiple?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Lowest Common Multiple?
Related topics in Mathematics include Negative Numbers, Adding and Subtracting Fractions, Decimals.