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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 432 432 = 216 • 2**

= 108 • 2 • 2 = 54 • 2 • 2 • 2 = 27 • 2 • 2 • 2 • 2 = 9 • 3 • 2 • 2 • 2 • 2 = 3 • 3 • 3 • 2 • 2 • 2 • 2 =33 • 24

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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 117 27 = 3 • 3 • 3, 117 = 13 • 3 • 3 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 117 27 = 3 • 3 • 3 = 33, 117 = 13 • 3 • 3 = 13 • 32 Take the largest factors of each number LCM = 33 • 13 = 351

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**Try These! find the GCF and LCM**

16a4b3 and 12a2b 21a2b5, 14a3b3, and 35a2b2 4, 240 Solution 11, 330 Solution 5, 6300 Solution 4a2b, 48a4b3 Solution 7a2b2, 210a3b5 Solution End Show

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80 and 12 80 = 40 • 2 80 = 20 • 2 • 2 80 = 10 • 2 • 2 • 2 80 = 5 • 2 • 2 • 2 • 2 80 = 5 • 24 12 = 6 • 2 12 = 3 • 2 • 2 12 = 3 • 22 GCF = 4 LCM = 5 • 24 • 3 = 240 Back to Try These!

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110 and 33 110 = 11 • 5 • 2 33= 3 • 11 GCF = 11 LCM = 11 • 5 • 2 • 3 LCM = 330 Back to Try These!

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45, 100, and 70 45 = 32 • 5 100 = 52 • 22 70 = 7 • 5 • 2 GCF = 5 LCM = 6300 Back to Try These!

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**16a4b3 and 12a2b 16a4b3 = 24 • a4 • b3 12a2b = 22 • 3 • a2 • b**

GCF = 22 • a2 • b GCF = 4a2b LCM = 24 • 3 • a4 • b3 LCM = 48a4b3 Back to Try These!

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**21a2b5, 14a3b3, and 35a2b2 21a2b5 = 7•3•a2•b5 14a3b3 = 7•2•a3•b3**

GCF = 7•a2•b=7a2b LCM = 7•5•2•3•a3•b5 LCM = 210a3b5 Back to Try These!

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