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

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Presentation on theme: "GCF and LCM Section 2.3 Standards Addressed: A1.1.1.5, A1.1.1.5.2."— Presentation transcript:

1 GCF and LCM Section 2.3 Standards Addressed: A , A

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 m 3 n 2 – 6m 2 n Example 3: Factor


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