Least Common Multiple.

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Presentation transcript:

Least Common Multiple

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

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, ...

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.

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, ...

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

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

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

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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, ...

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, ...

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

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

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

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

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

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