GCF and LCM Section 2.3 Standards Addressed: A , A

 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

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

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

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

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

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

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

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

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

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

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

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

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.

Polynomial:21x 2 – 28xy 3

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

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

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

(B) 8m 4 n m 3 n 2 – 6m 2 n Example 3: Factor