The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 6.7: FINDING THE LEAST COMMON MULTIPLE

OF POLYNOMIALS

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Follow the steps below to find the least common multiple (LCM) of polynomials:

1. Factor each polynomial.


2. Write the product of each factor, raised to the highest number of times it is a factor of
   one of the polynomials.

EXAMPLE

Find the LCM ofx^2 − 4 andx^2 − 4 x+ 4.

Factor.x^2 − 4 =(x−2)(x+2)andx^2 − 4 x+ 4 =(x−2)(x−2)or(x−2)^2.

(x− 2 )and(x+ 2 ) are the factors. The highest power of (x+ 2 ) is 1. The highest power of

(x− 2 ) is 2. Therefore,(x+2)(x−2)^2 is the LCM.

DIRECTIONS: Find the LCM of the polynomials.

1. x^2 − 5 x+6andx^2 − 6 x+ 8 2.x^2 −16 andx^2 + 2 x− 8

3.x^2 − 10 x+25 andx^2 −x− 20 4.x^2 + 3 x−4andx^2 + 6 x+ 8

5. x^2 + 8 x+16 andx^2 + 5 x+ 4 6.x^3 +x^2 andx^2 + 7 x+ 6


6. 5 x^2 +50 andx^2 + 10 8.x^2 + 3 x−4andx^2 + 10 x+ 16

CHALLENGE:Deena factored two polynomials and found that the polynomials

had no factors in common. She concluded that the LCM of the polynomials

was the same as the product of the factors. Do you agree? Explain your

reasoning.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.