1. GCF and LCM Section 2.3 Standards Addressed: A1.1.1.5, A1.1.1.5.2

2.  How can we use a greatest common factor of two or more monomials to solve problems?  How can we use a least common multiple of two or more monomials to solve problems?  When do we need to use a greatest common factor to model a situation?  When do we need to use a least common multiple to model a situation? Essential Questions

3. You can find the Greatest Common Factor (GCF) of two or more monomials by finding the product of their common prime factors.

4. Find the GCF of 16xy 2 and 30xy 3 Example 1

5. Find the GCF of 16xy 2 and 30xy 3 Example 1 16xy 2 : 2  2  2  2  x  y  y 30xy 3 : 2  3  5  x  y  y  y

6. Find the GCF of 16xy 2 and 30xy 3 Example 1 16xy 2 : 2  2  2  2  x  y  y 30xy 3 : 2  3  5  x  y  y  y

7. Find the GCF of 16xy 2 and 30xy 3 Example 1 16xy 2 : 2  2  2  2  x  y  y 30xy 3 : 2  3  5  x  y  y  y The GCF of 16xy 2 and 30xy 3 is 2xy 2

8. You can find the Least Common Multiple (LCM) of two or more monomials by multiplying the factors, using the common factors only once.

9. Find the LCM of 18xy 2 and 10y Example 2

10. Find the LCM of 18xy 2 and 10y Example 2 18xy 2 : 2  3  3  x  y  y 10y: 2  5  y

11. Find the LCM of 18xy 2 and 10y Example 2 18xy 2 : 2  3  3  x  y  y 10y: 2  5  y

12. Find the LCM of 18xy 2 and 10y Example 2 18xy 2 : 2  3  3  x  y  y 10y: 2  5  y LCM: 2  3  3  5  x  y  y

13. Find the LCM of 18xy 2 and 10y Example 2 18xy 2 : 2  3  3  x  y  y 10y: 2  5  y LCM: 2  3  3  5  x  y  y The LCM of 18xy 2 and 10y is 90xy 2

14. To factor a polynomial means to write the polynomial as a product of other polynomials. First, find the GCF of its terms (if the GCF exists). Next, use the distributive property to write the polynomial in factored form.

15. Polynomial:21x 2 – 28xy 3

16. Polynomial:21x 2 – 28xy 3 Find the GCF of terms:7x(3x) – 7x(4y 3 )

17. Polynomial:21x 2 – 28xy 3 Find the GCF of terms:7x(3x) – 7x(4y 3 ) Use the Distributive Property:7x(3x – 4y 3 )

18. (A) 3x 3 y – 15x 2 y 4 Example 3: Factor

19. (B) 8m 4 n 2 + 18m 3 n 2 – 6m 2 n Example 3: Factor