Least Common Multiples

Least Common Multiples

Least Common Multiple (LCM) The least common multiple is the smallest number that is common between two lists of multiples.

EXAMPLE: Find the LCM of 12 and 18 The multiples of 12: The multiples of 18: 12 x 1 12 18 x 1 18 12 x 2 24 18 x 2 36 12 x 3 36 18 x 3 54 12 x 4 48 18 x 4 72 12 x 5 60 18 x 5 90

12, 24, 36, 48, 60 18, 36, 54, 72, 90 The first number you see in both lists is 36. The least common multiple of 12 and 18 is 36.

Example 2: Find the LCM of 9 and 10 9, 18, 27, 36, 45, 54, 63, 72 81, 90, 99 10, 20, 30, 40, 50, 60, 70, 80 90, 100, 110 If you don’t see a common multiple, make each list go further. The LCM of 9 and 10 is 90

Example 3: Find the LCM of 4 and 12 4, 8, 12, 16 12, 24, 36 Answer: 12

Example 4: Find the LCM of 5 and 8 5, 10, 15, 20, 25, 30 35, 40 8, 16, 24, 32, 40, 48 Answer: 40

Example 5: Find the LCM of 6 and 20 6, 12, 18, 24, 30, 36 42, 48, 54, 60 20, 40, 60, 80, 100, 120 Answer: 60