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# GCF and LCM Section 2.3 Standards Addressed: A1.1.1.5 , A1.1.1.5.2 - PowerPoint PPT Presentation

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

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GCF and LCMSection 2.3Standards Addressed: A1.1.1.5, A1.1.1.5.2

• 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

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 16 monomials by finding the product of their common prime factors.xy2 and 30xy3

Example 1

Find the GCF of 16 monomials by finding the product of their common prime factors.xy2 and 30xy3

16xy2: 2  2  2  2 x y y

30xy3: 2 3  5 xyy y

Example 1

Find the GCF of 16 monomials by finding the product of their common prime factors.xy2 and 30xy3

16xy2: 2  2  2  2 x y y

30xy3: 2 3  5 xyy y

Example 1

Find the GCF of 16 monomials by finding the product of their common prime factors.xy2 and 30xy3

16xy2: 2  2  2  2 x y y

30xy3: 2 3  5 xyy y

Example 1

The GCF of 16xy2 and 30xy3 is 2xy2

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 18 monomials by multiplying the factors, using the common factors only once.xy2 and 10y

Example 2

Find the LCM of 18 monomials by multiplying the factors, using the common factors only once.xy2 and 10y

18xy2: 2  3  3 x y y

10y: 2  5y

Example 2

Find the LCM of 18 monomials by multiplying the factors, using the common factors only once.xy2 and 10y

18xy2: 2  3  3 x y y

10y: 2  5y

Example 2

Find the LCM of 18 monomials by multiplying the factors, using the common factors only once.xy2 and 10y

18xy2: 2  3  3 x y y

10y: 2  5y

LCM: 2  3  3  5 x y y

Example 2

Find the LCM of 18 monomials by multiplying the factors, using the common factors only once.xy2 and 10y

18xy2: 2  3  3 x y y

10y: 2  5y

LCM: 2  3  3  5 x y y

Example 2

The LCM of 18xy2 and 10y is 90xy2

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: 21 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.x2 – 28xy3

Polynomial: 21 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.x2 – 28xy3Find the GCFof terms: 7x(3x) – 7x(4y3)

Polynomial: 21 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.x2 – 28xy3Find the GCFof terms: 7x(3x) – 7x(4y3)Use theDistributiveProperty: 7x(3x – 4y3)

(A) 3 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.x3y – 15x2y4

Example 3: Factor

(B) 8 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.m4n2 + 18m3n2 – 6m2n

Example 3: Factor