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Least Common Multiple LCM 2 Methods copyright©amberpasillas2010 Product The answer to a multiplication problem. 6 X 6 = 36 copyright©amberpasillas2010 What is the product? 7 X 8 = 56 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 copyright©amberpasillas2010 Name the first six multiples of 5 5, 10, 15, 20, 25, 30 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 4 = 4, 8, 12, 16, 20, 24 10 = 10, 20, 30, 40, 50, copyright©amberpasillas2010 Least Common Multiple LCM - Least Common Multiple - Smallest number that a set of given numbers divides evenly into. 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 copyright©amberpasillas2010 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. 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 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 copyright©amberpasillas2010 What is the Least Common Multiple of 4 & 10 4 = 4, 8, 12, 16, 20, 24 10 = 10, 20, 30, 40, 50, copyright©amberpasillas2010 What is the Least Common Multiple of 6 & 8 6 = 6, 12, 18, 24, 30, 36 8 = 8, 16, 24, 32, 40, 48 copyright©amberpasillas2010 What is the Least Common Multiple of 3 & 9 3 = 3, 6, 9, 12, 15, 21, 9 = 9, 18, 27, 36, 45, 54 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 copyright©amberpasillas2010 Least Common Multiple Method # 2 1) Write the prime factorization of each number. 2) Select all common factors ONCE. 3) Then select the remaining factors and multiply. copyright©amberpasillas2010 Least Common Multiple Method # 2 18 2 20 2 10 9 3 3 2 3 3 2 5 2 25 Select all common factors once. Then select the remaining factors. LCM 2 3 32 5 LCM 180 copyright©amberpasillas2010 Least Common Multiple Method # 2 45 5 72 9 3 8 3 3 3 5 9 2 4 3 3 2 2 2 2 2 3 3 Select all common factors once. Then select the remaining factors. LCM 3 35 2 2 2 LCM 360 copyright©amberpasillas2010 Least Common Multiple Method # 2 Find the LCM of 48 and 80. 48 2 Common 2 24 Factors 2 12 Once 2 6 3 80 40 20 10 5 Remaining Factors LCM 2 2 2 2 3 5 LCM 240 copyright©amberpasillas2010 Least Common Multiple Method # 2 SO I GUESS YOU ARE WONDERING When Are We Ever Gonna Have To Use This? copyright©amberpasillas2010 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. 3 5 3 8 15 24 7 2 12 2 14 24 copyright©amberpasillas2010 2 8 2 4 2 12 6 3 LCM 2 2 2 3 LCM 24 Least Common Multiple Method # 2 The GCF and LCM are used so regularly that most people find them mentally. GCF = 1 1) 8 GCF = 5 9 2) LCM = 72 15 20 LCM = 60 copyright©amberpasillas2010 copyright©amberpasillas2010 Least Common Multiple Method # 2 The GCF and LCM are used so regularly that most people find them mentally. GCF = 4 1) 12 GCF = 4 20 2) LCM = 60 8 12 LCM = 24 copyright©amberpasillas2010 copyright©amberpasillas2010 Least Common Multiple Method # 2 THE END Take Out Your Study Guide!!! 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. 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. copyright©amberpasillas2010 #10 LCM Make a List Method # 1 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. copyright©amberpasillas2010 #11 LCM Prime Factorization Method # 2 1) List the prime factorization to find the LCM. 20 18 2 2 10 9 3 3 2 2 3 3 2) 3) 5 2 25 Select all common factors once. Select all remaining factors, and multiply. LCM 180 LCM 2 332 5 copyright©amberpasillas2010