Least Common Multiple
The LCM is the smallest number that both numbers divide into.
About this topic
The least common multiple (LCM) is the smallest positive number that is a multiple of each of the given numbers. For 4 and 6 it is 12. List the multiples of each until one appears in both, or use prime factorizations and take the highest power of each prime.
The LCM is what you need to find a common denominator when adding fractions, and to predict when repeating events line up again, like two blinking lights. A handy link: for two numbers, LCM × GCD equals their product. For 4 and 6, the GCD is 2 and 4 × 6 = 24 = 12 × 2.
Consider adding 1/4 and 1/6. The LCM of 4 and 6 is 12, so rewrite them as 3/12 and 2/12, giving 5/12. Using the LCM rather than just the product keeps the numbers smaller and saves simplifying later. In scheduling, if one planet-watching club meets every 9 days and another every 12 days, they meet together every 36 days, since 36 is the LCM of 9 and 12.
With prime factorization, 9 = 3² and 12 = 2² × 3, so take 2² and 3² to get 36. A common mistake is taking the lowest power, which gives the GCD instead, or listing multiples and stopping at the first one that works for only one of the numbers. Always check that your answer divides evenly by each original number.
Key ideas
- List multiples until they first match
- LCM × GCD equals the product of the two numbers
- Used to find common denominators
Quick check
Use cases: where Least Common Multiple helps
- Homework: review the key idea behind Least Common Multiple before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Least Common Multiple without notes.
- Visual learning: play with the interactive lab to see how Least Common Multiple changes when you adjust its inputs.
- Teaching a friend: explain Least Common Multiple in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Least Common Multiple?
The LCM is the smallest number that both numbers divide into.
What will I learn in Least Common Multiple?
List multiples until they first match. LCM × GCD equals the product of the two numbers. Used to find common denominators.
Is Least Common Multiple part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Least Common Multiple lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Least Common Multiple?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.