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Least Common Multiple

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**A multiple of a number is the product of the number and any whole number.**

6 x 0 = 0 6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54

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6 x 0 = 0 6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 The multiples of 6 are: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, ...

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**The Least Common Multiple is the smallest multiple that two or more numbers have in common.**

To find the LCM of two or more numbers you can make a list of multiples or use prime factorization.

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**Make a list of several multiples of the numbers.**

Make a list of multiples: Find the LCM of 4 and 6. Make a list of several multiples of the numbers. Multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, ... Multiples of 6: 0, 6, 12, 18, 24, 30, 36, ...

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4, 8, 12, 16, 20, 24, 28, 32, 36, ... 6, 12, 18, 24, 30, 36, ... Identify the common multiples of 4 and 6.

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4, 8, 12, 16, 20, 24, 28, 32, 36, ... 6, 12, 18, 24, 30, 36, ... Identify the common multiples of 4 and 6.

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4, 8, 12, 16, 20, 24, 28, 32, 36, ... 6, 12, 18, 24, 30, 36, ... Identify the common multiples of 4 and 6.

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4, 8, 12, 16, 20, 24, 28, 32, 36, ... 6, 12, 18, 24, 30, 36, ... Identify the common multiples of 4 and 6.

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4, 8, 12, 16, 20, 24, 28, 32, 36, ... 6, 12, 18, 24, 30, 36, ... The common multiples are 12, 24 and 36. The LCM of 4 and 6 is 12 . LCM = 12

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Find the LCM of 15 and 9. 15, 30, 45, 60, 75, ... 9, 18, 27, 36, 45, 54, ...

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Find the LCM of 15 and 9. 15, 30, 45, 60, 75, ... 9, 18, 27, 36, 45, 54, ... Find the common multiples of 15 and 9.

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Find the LCM of 15 and 9. 15, 30, 45, 60, 75, ... 9, 18, 27, 36, 45, 54, ... Find the common multiples of 15 and 9.

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Find the LCM of 15 and 9. 15, 30, 45, 60, 75, ... 9, 18, 27, 36, 45, 54, ... The LCM of 15 and 9 is 45. LCM = 45

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Find the LCM of 6 and 9. 6, 12, 18, 24, 30, 36, ... 9, 18, 27, 36, 45, 54, ...

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Find the LCM of 6 and 9. 6, 12, 18, 24, 30, 36, ... 9, 18, 27, 36, 45, 54, ...

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Find the LCM of 6 and 9. 6, 12, 18, 24, 30, 36, ... 9, 18, 27, 36, 45, 54, ...

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Find the LCM of 6 and 9. 6, 12, 18, 24, 30, 36, ... 9, 18, 27, 36, 45, 54, ... LCM = 18

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Find the LCM of 6 and 12. 6, 12, 18, 24, 30, 36, ... 12, 24, 36, ...

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Find the LCM of 6 and 12. 6, 12, 18, 24, 30, 36, ... 12, 24, 36, ...

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Find the LCM of 6 and 12. 6, 12, 18, 24, 30, 36, ... 12, 24, 36, ...

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Find the LCM of 6 and 12. 6, 12, 18, 24, 30, 36, ... 12, 24, 36, ... LCM = 12

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Find the LCM of 4, 6 and 8. 4, 8, 12, 16, 20, 24, 28, ... 6, 12, 18, 24, 30, 36, ... 8, 16, 24, 32, 40, ...

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Find the LCM of 4, 6 and 8. 4, 8, 12, 16, 20, 24, 28, ... 6, 12, 18, 24, 30, 36, ... 8, 16, 24, 32, 40, ...

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Find the LCM of 4, 6 and 8. 4, 8, 12, 16, 20, 24, 28, ... 6, 12, 18, 24, 30, 36, ... 8, 16, 24, 32, 40, ... LCM = 24

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**LCM using prime factorization:**

Step 1: Prime factor the numbers. 24 18 ^ ^ 6 x 3 4 x 6 ^ ^ ^ 2 x 3 2 x 2 2 x 3

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**LCM using prime factorization:**

Step 1: Prime factor the numbers. 24 18 ^ ^ 6 x 3 4 x 6 ^ ^ ^ 2 x 3 2 2 x 3 x 2 Step 2: Draw a grid and place the factors in the grid. 24 = 18 = 2 2 2 3 2 3 3

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**Step 3: Bring one factor down from each column.**

24 = 18 = 2 2 2 3 2 3 3 2 x 2 x 2 x 3 x 3 4 x 2 x 3 x 3 8 x 3 x 3 24 x 3 LCM = 72

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**Find the LCM of 16 and 24 using prime factors.**

16 = 24 = 2 2 2 3 2 x 2 x 2 x 2 x 3 LCM = 48

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**Find the LCM of 6, 8, and 12 using prime factors.**

6 = 8 = 12 = 2 3 2 2 2 2 3 2 2 x 3 x 2 x 2 LCM = 24

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