LCM = Least Common Multiple

The number that is the smallest number that a problem has in common is called the least common multiple. We use LCM when we find the least common denominator when adding or subtracting fraction problems.

A MULTIPLE is a number that is the answer to a multiplication problem.

Problem: Find the LCM (Least Common Multiple) of 3 and 4.

Solution:

First write a list of multiples starting with a multiplier of 1 and count upward:

Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, etc.

Multiples of 4 are: 4, 8, 12, 16, 20, 24, 27, 32, 36, 40, 44, 48, 52, etc.

The numbers that appear in BOTH lists are called COMMON FACTORS.

These numbers that are common to BOTH lists are: 12, 24, 48, etc.

The LEAST COMMON MULTIPLE is the SMALLEST number in the list above.

The LCM is 12.

Problem: Find the LCM of 3, 15 and 9.

Solution:

Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, etc.

Multiples of 15 are: 15, 30, 45, 60, 75, 90, 105, etc.

Multiples of 9 are: 9, 18, 27, 36, 45, 54, 63 etc.

Usually, when the problem has large numbers like this one, you can stop making the multiples list when you see the first number that they have in common as it is the LEAST common multiple of the problem. If you continued to make the list for 3, you’d see 90 as one of the common multiples BUT 90 is not the smallest number and 45 is smallest they have in common.

In this problem, the LCM is 45.