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**Least Common Multiple (LCM)**

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

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**3 Methods for finding the LCM**

Method 1: Use a number line Ex. 3 & 4 Method 2: Use a list 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72 Method 3: Use Prime Factorization Ex. 8 & 12 8 = 2 • 2 • 2 12 = 2 • 2 • 3 2 • 2 • 3 • 2 = LCM of 8 & 12

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**More Method 2 Examples: (2 numbers)**

2 & 8 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 LCM = 8 4 & 10 4: 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

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**More Method 3 Examples: (2 numbers)**

4 & 9 4= 2 • 2 9= 3 • 3 3 • 3 • 2 • 2 = 36 6 & 10 6= 2 • 3 10= 2 • 5 2 • 5 • 3 = 30 * LCM for 4 & 9 is 36 * LCM for 6 & 10 is 30

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**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, , 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68 6: 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, & 12 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 LCM = 24

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**More Method 3 Examples: (3 numbers)**

3, 7 & 10 3= 3 7= 7 10= 2•5 2•5 • 7 • 3 = 210 3, 6 ,& 9 6= 3 • 2 9= 3 • 3 3 • 3 • 2 = 18 * LCM for 3, 7, & 10 is 210 * LCM for 3, 6, & 9 is 18

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