Least Common Multiple

Least Common Multiple (LCM) - The least common multiple of two or more numbers is the smallest number (excluding zero) that is a multiple of all of them.

Example: Find the LCM of 6 and 8.

The multiples of 6 are 6, 12, 18, 24, 30
The multiples of 8 are 8, 16, 24, 32, 40

24 is the least common multiple (LCM) of 6 and 8. An easy way to find all the multiples of a specific number is to just count by that number. Example, to find the multiples of 5 you would do 5, 10, 15, 20, 25, 30, etc. Easy enough.

Another characteristic of the least common multiple (LCM) of two or more numbers is that it is the smallest whole number that can be evenly divided by each of the numbers.

Another way to find the LCM is to find the PRIME FACTORIZATION of each number.

Example: Find the LCM of 12 and 15.

1. Factor each of the numbers into its prime factors.
12 = 2 x 2 x 3
15 = 3 x 5

2. For each prime, find the MOST number of times it is used in any one factorization.
12 = 2 x 2 x 3
15 = 3 x 5
2 appears twice, 3 appears once, and 5 appears once.

3. Multiply these prime factors together to get the LCM.
LCM = 2 x 2 x 3 x 5 = 60

That's the trick for bigger numbers.

Another side note: The least common multiple (LCM) is t he same as the least (or lowest) common denominator (LCD). The LCD is used to rename or change unlike fractions to like fractions in the addition and subtraction of fractions and mixed numbers.