What is the Least Common Multiple (LCM)?
The smallest number that a given group of numbers will divide into evenly
The Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. In other words, it’s the first number that appears in all their multiplication tables.
For example, the LCM of 4 and 5 is 20 because 20 is the smallest number that both 4 and 5 divide into evenly:
- 4 × 5 = 20
- 5 × 4 = 20
We use the LCM when:
- Finding common denominators to add or subtract fractions
- Solving problems with repeating events or schedules
- Working with patterns and multiples
When Do Students Learn About the Least Common Multiple?
Students are introduced to the concept of multiples in the upper elementary grades, and they begin applying the LCM in real-world and algebraic contexts as they progress.
Grades 4–5 – Introduction to Multiples and LCM
Students learn to list multiples of numbers and find the LCM to solve basic problems, especially involving fractions.
Grades 6+ – Applying LCM in Fractions and Algebra
Students use the LCM to solve more complex fraction and ratio problems and begin applying it to algebraic expressions.
