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

2. 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)

3. 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

4. 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

5. 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

6. 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

7. 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!

8. 110 and 33
110 = 11 • 5 • 2
33= 3 • 11
GCF = 11
LCM = 11 • 5 • 2 • 3 LCM = 330
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9. 45, 100, and 70
45 = 32 • 5
100 = 52 • 22
70 = 7 • 5 • 2
GCF = 5
LCM = 6300
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10. 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
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11. 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
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