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**Least Common Multiple LCM 2 Methods**

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Product The answer to a multiplication problem. 6 X 6 = 36

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What is the product? 7 X 8 = 56

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**Name the first six multiples of 6**

The product of a whole number multiplied times any other whole number. Name the first six multiples of 6 6, 12, 18, 24, 30, 36

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**Name the first six multiples of 5**

5, 10, 15, 20, 25, 30

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Common Multiple A Common Multiple is a number that is a multiple of two numbers. Here are common multiples for the numbers 4 and 10 4 = 4, 8, 12, 16, 20, 24 10 = 10, 20, 30, 40, 50,

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Least Common Multiple LCM - Smallest number that a set of given numbers divides evenly into. Least Common Multiple - It is useful to know how to do this so you can find a common denominator when adding or subtracting fractions. THERE ARE TWO WAYS TO FIND LCM

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**Least Common Multiple Method # 1**

TO FIND THE LCM OF TWO NUMBERS List the multiples of both numbers Find the least multiple that both numbers have in common.

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**Least Common Multiple Method # 1**

Make a List of Multiples Find the LCM of 10 and 12. 10: 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 ... 12: 12 , 24 , 36 , 48 , 60 LCM = 60

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**Least Common Multiple Method # 1**

Make a List of Multiples Find the LCM of 32 and 40. 32: 32 , 64 , 96 , 128 , 160 , 192 , 224 , 256 ... 40: 40 , 80 , 120 , 160 LCM = 160

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**What is the Least Common Multiple of 4 & 10**

4 = 4, 8, 12, 16, 20, 24 10 = 10, 20, 30, 40, 50,

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**What is the Least Common Multiple of 6 & 8**

6 = 6, 12, 18, 24, 30, 36 8 = 8, 16, 24, 32, 40, 48

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**What is the Least Common Multiple of 3 & 9**

3 = 3, 6, 9, 12, 15, 21, 9 = 9, 18, 27, 36, 45, 54

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Method #1 is easy to do! Method #1 is a good method if both of your numbers are really small. What if you have really large numbers? It might take too long to keep listing multiples until you find a common multiple. SO HERE IS METHOD # 2

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**Least Common Multiple Method # 2**

1) Write the prime factorization of each number. Select all common factors ONCE. 3) Then select the remaining factors and multiply.

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**Least Common Multiple Method # 2**

18 20 2 9 2 10 3 3 2 5 Select all common factors once. Then select the remaining factors.

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**Least Common Multiple Method # 2**

45 72 5 9 8 9 3 3 2 4 3 3 2 2 Select all common factors once. Then select the remaining factors.

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**Least Common Multiple Method # 2**

Find the LCM of 48 and 80. 2 Common Factors Once 2 2 2 Remaining Factors

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**SO I GUESS YOU ARE WONDERING**

Least Common Multiple Method # 2 SO I GUESS YOU ARE WONDERING When Are We Ever Gonna Have To Use This?

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**Least Common Multiple Method # 2**

What is the LCM used for? The LCM is used to find common denominators so that fractions may be easily compared, added, or subtracted.

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**Least Common Multiple Method # 2**

The GCF and LCM are used so regularly that most people find them mentally. GCF = 1 GCF = 5 1) 2) LCM = 72 LCM = 60 copyright©amberpasillas2010

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**Least Common Multiple Method # 2**

The GCF and LCM are used so regularly that most people find them mentally. GCF = 4 GCF = 4 1) 2) LCM = 60 LCM = 24 copyright©amberpasillas2010

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**Least Common Multiple Method # 2**

THE END Take Out Your Study Guide!!!

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**#9 Multiples A number that is added to itself becomes a multiple.**

3, 6, 9, 12, 15, Multiples of 3 = Multiples can go on infinitely forever. The least common multiple (LCM) is the least common number that is a multiple of 2 numbers. It is useful to know this for adding fractions.

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**LCM is 12 LCM Make a List Method # 1 4 = 4, 8, 12, 16, 20…**

#10 TO FIND THE LCM OF 4 and 12: 1) List the multiples of both numbers 4 = 4, 8, 12, 16, 20… 12 = 12, 24, 36… 2) Find the least multiple that both numbers have in common. LCM is 12 This method is useful if both numbers are small.

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**18 20 2 9 2 10 3 3 2 5 #11 LCM Prime Factorization Method # 2**

1) List the prime factorization to find the LCM. 18 20 2 9 2 10 3 3 2 5 2) Select all common factors once. 3) Select all remaining factors, and multiply.

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We need a common denominator to add these fractions.

We need a common denominator to add these fractions.

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