What is a Least Common Multiple (LCM)?
The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is a multiple of all the numbers.
Explanation:
- A multiple of a number is the product of that number and an integer. For example, multiples of 3 are 3, 6, 9, 12, and so on.
- The LCM is the smallest number that appears in the list of multiples of each number.
Example:
Find the LCM of 4 and 6.
- Multiples of 4: 4, 8, 12, 16, 20, ...
- Multiples of 6: 6, 12, 18, 24, 30, ...
The smallest common multiple is 12 , so the LCM of 4 and 6 is 12.
Why is LCM useful?
- It helps in adding, subtracting, or comparing fractions with different denominators.
- It is used in solving problems involving repeated events or cycles.
If you'd like, I can also show you how to find the LCM using prime factorization or other methods!