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Using Prime Factorization Objective: To find the GCF and LCM of integers and monomials

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Prime Numbers An integer greater than 1 whose only factors are its self and one. Examples: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29…} Real life application: cryptography (code breaking)

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Example: Find the prime factorization of = = = = = = =

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Greatest Common Factor (GCF) The greatest integer that is a factor of each integer. Example: find the GCF of 27 and = 3 3 3, 117 = GCF = 3 3 = 9

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Least Common Multiple (LCM) Least positive integer having each as a factor Example: Find the least common multiple of 27 and = = 3 3, 117 = = Take the largest factors of each number LCM = = 351

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Try These! find the GCF and LCM 1.80 and and , 100, and a 4 b 3 and 12a 2 b 5.21a 2 b 5, 14a 3 b 3, and 35a 2 b 2 4, 240 Solution 11, 330 Solution Solution 5, 6300 Solution Solution 4a 2 b, 48a 4 b 3 Solution Solution 7a 2 b 2, 210a 3 b 5 Solution Solution End Show

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80 and = = = = = = = GCF = 4 LCM = = 240 Back to Try These!

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110 and = = 3 11 GCF = 11 LCM = LCM = 330 Back to Try These!

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45, 100, and = = = GCF = 5 LCM = 6300 Back to Try These!

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16a 4 b 3 and 12a 2 b 16a 4 b 3 = 2 4 a 4 b 3 12a 2 b = a 2 b GCF = 2 2 a 2 b GCF = 4a 2 b LCM = a 4 b 3 LCM = 48a 4 b 3 Back to Try These!

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21a 2 b 5, 14a 3 b 3, and 35a 2 b 2 21a 2 b 5 = 73a 2 b 5 14a3b3 = 72a 3 b 3 35a 2 b 2 = 75a 2 b 2 GCF = 7a 2 b=7a 2 b LCM = 7523a 3 b 5 LCM = 210a 3 b 5 Back to Try These!

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