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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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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

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

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

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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

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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

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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

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

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

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

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

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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

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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

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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.

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Polynomial:21x 2 – 28xy 3

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

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

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

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

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Finding the LCM (least common multiple) and GCF (greatest common factor)

Finding the LCM (least common multiple) and GCF (greatest common factor)

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