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Martin-Gay, Beginning Algebra, 5ed 22

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10 Example For each pair of polynomials, find the least common multiple. a) 16a and 24b b) 24x 4 y 4 and 6x 6 y 2 c) x 2 4 and x 2 2x 8 Solution a) 16a = 2 2 2 2 a 24b = 2 2 2 3 b The LCM = 2 2 2 2 a 3 b The LCM is 2 4 3 a b, or 48ab 16a is a factor of the LCM 24b is a factor of the LCM

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Martin-Gay, Beginning Algebra, 5ed 11 Example continued b) 24x 4 y 4 = 2 2 2 3 x x x x y y y y 6x 6 y 2 = 2 3 x x x x x x y y LCM = 2 2 2 3 x x x x y y y y x x Note that we used the highest power of each factor. The LCM is 24x 6 y 4 c) x 2 4 = (x 2)(x + 2) x 2 2x 8 = (x + 2)(x 4) LCM = (x 2)(x + 2)(x 4) x 2 4 is a factor of the LCM x 2 2x 8 is a factor of the LCM

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Martin-Gay, Beginning Algebra, 5ed 12 a) b) c) d) e)

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