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copyright©amberpasillas2010 Least Common Multiple LCM 2 Methods

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copyright©amberpasillas2010 Product The answer to a multiplication problem. 6 X 6 = 36

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copyright©amberpasillas2010 What is the product? 7 X 8 = 56

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copyright©amberpasillas2010 Multiple 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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copyright©amberpasillas2010 Name the first six multiples of 5 5, 10, 15, 20, 25, 30

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copyright©amberpasillas2010 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 10 = 10, 20, 30, 40, 50, 4 = 4, 8, 12, 16, 20, 24

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copyright©amberpasillas2010 Least Common Multiple Smallest number that a set of given numbers divides evenly into. LCM -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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copyright©amberpasillas2010 Least Common Multiple Method # 1 TO FIND THE LCM OF TWO NUMBERS Find the least multiple that both numbers have in common. List the multiples of both numbers

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copyright©amberpasillas2010 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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copyright©amberpasillas2010 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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copyright©amberpasillas2010 What is the Least Common Multiple of 4 & 10 10 = 10, 20, 30, 40, 50, 4 = 4, 8, 12, 16, 20, 24

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copyright©amberpasillas2010 What is the Least Common Multiple of 6 & 8 8 = 8, 16, 24, 32, 40, 48 6 = 6, 12, 18, 24, 30, 36

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copyright©amberpasillas2010 What is the Least Common Multiple of 3 & 9 9 = 9, 18, 27, 36, 45, 54 3 = 3, 6, 9, 12, 15, 21,

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copyright©amberpasillas2010 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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copyright©amberpasillas2010 1) Write the prime factorization of each number. 3) Then select the remaining factors and multiply. 2) Select all common factors ONCE. Least Common Multiple Method # 2

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copyright©amberpasillas2010 20 2 10 2 5 18 2 9 3 3 Select all common factors once. Then select the remaining factors. Least Common Multiple Method # 2

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copyright©amberpasillas2010 45 5 9 3 3 Select all common factors once. Then select the remaining factors. 72 8 9 3 3 2 4 2 2 Least Common Multiple Method # 2

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copyright©amberpasillas2010 Find the LCM of 48 and 80. 48 80 2 24 40 2 12 20 2 6 102 3 5 Common Factors Once Remaining Factors Least Common Multiple Method # 2

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copyright©amberpasillas2010 SO I GUESS YOU ARE WONDERING When Are We Ever Gonna Have To Use This? Least Common Multiple Method # 2

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copyright©amberpasillas2010 What is the LCM used for? The LCM is used to find common denominators so that fractions may be easily compared, added, or subtracted. Least Common Multiple Method # 2

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copyright©amberpasillas2010 The GCF and LCM are used so regularly that most people find them mentally. GCF =1 LCM = 72 GCF = 5 LCM = 60 1) 8 9 2) 15 20 copyright©amberpasillas2010 Least Common Multiple Method # 2

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copyright©amberpasillas2010 The GCF and LCM are used so regularly that most people find them mentally. GCF =4 LCM = 60 GCF = 4 LCM = 24 1) 12 20 2) 8 12 copyright©amberpasillas2010 Least Common Multiple Method # 2

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copyright©amberpasillas2010 THE END Take Out Your Study Guide!!! Least Common Multiple Method # 2

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copyright©amberpasillas2010 #9 Multiples A number that is added to itself becomes a multiple. Multiples of 3 = 3, 6, 9, 12, 15, 18... Multiples can go on infinitely forever. It is useful to know this for adding fractions. The least common multiple (LCM) is the least common number that is a multiple of 2 numbers.

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copyright©amberpasillas2010 LCM Make a List Method # 1 TO FIND THE LCM OF 4 and 12: 2) Find the least multiple that both numbers have in common. 1) List the multiples of both numbers 4 = 4, 8, 12, 16, 20… 12 = 12, 24, 36… LCM is 12 #10 This method is useful if both numbers are small.

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copyright©amberpasillas2010 1) List the prime factorization to find the LCM. 20 2 10 2 5 18 2 9 3 3 2) Select all common factors once. 3) Select all remaining factors, and multiply. #11 LCM Prime Factorization Method # 2

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