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


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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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essential questions

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
slide3
You can find the Greatest Common Factor (GCF) of two or more monomials by finding the product of their common prime factors.
example 11

Find the GCF of 16xy2 and 30xy3

16xy2: 2  2  2  2 x y y

30xy3: 2 3  5 xyy y

Example 1
example 12

Find the GCF of 16xy2 and 30xy3

16xy2: 2  2  2  2 x y y

30xy3: 2 3  5 xyy y

Example 1
example 13

Find the GCF of 16xy2 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

slide8
You can find the Least Common Multiple (LCM) of two or more monomials by multiplying the factors, using the common factors only once.
example 21

Find the LCM of 18xy2 and 10y

18xy2: 2  3  3 x y y

10y: 2  5y

Example 2
example 22

Find the LCM of 18xy2 and 10y

18xy2: 2  3  3 x y y

10y: 2  5y

Example 2
example 23

Find the LCM of 18xy2 and 10y

18xy2: 2  3  3 x y y

10y: 2  5y

LCM: 2  3  3  5 x y y

Example 2
example 24

Find the LCM of 18xy2 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

slide14

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.

slide17
Polynomial: 21x2 – 28xy3Find the GCFof terms: 7x(3x) – 7x(4y3)Use theDistributiveProperty: 7x(3x – 4y3)
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