The smallest number, other than zero, that is a multiple of two or more

given numbers

Least Common Multiple(LCM)

3 Methods for finding the LCM

Method 1: Use a number line Ex. 3 & 4

Method 2: Use a list3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 365: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 606: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

Method 3: Use Prime Factorization Ex. 8 & 128 = 2 • 2 • 2

12 = 2 • 2 • 3

2 • 2 • 3 • 2 = 24 LCM of 8 & 12

More Method 2 Examples: (2 numbers)

2 & 82: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 288: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

LCM = 8

4 & 104: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120

LCM = 20

More Method 3 Examples: (2 numbers)

4 & 94= 2 • 29= 3 • 3

3 • 3 • 2 • 2 = 36

6 & 106= 2 • 3

10= 2 • 5

2 • 5 • 3 = 30

* LCM for 4 & 9 is 36

* LCM for 6 & 10 is 30

More Method 2 Examples: (3 numbers)2, 6, & 11

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 686: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121

LCM = 66

3, 8, & 123: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 368: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120LCM = 24

More Method 3 Examples: (3 numbers)

3, 7 & 103= 37= 7

10= 2•5

2•5 • 7 • 3 = 210

3, 6 ,& 93= 36= 3 • 29= 3 • 3

3 • 3 • 2 = 18

* LCM for 3, 7, & 10 is 210

* LCM for 3, 6, & 9 is 18