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Example

For each pair of polynomials, find the least common multiple.a) 16a and 24bb) 24x4y4 and 6x6y2

c) x2 4 and x2 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 24 3 a b, or 48ab

16a is a factor of the LCM

24b is a factor of the LCM

Martin-Gay, Beginning Algebra, 5ed 1111

Example continued

b) 24x4y4 = 2 2 2 3 x x x x y y y y

6x6y2 = 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 24x6y4

c) x2 4 = (x 2)(x + 2)

x2 2x 8 = (x + 2)(x 4)

LCM = (x 2)(x + 2)(x 4)

x2 4 is a factor of the LCM

x2 2x 8 is a factor of the LCM

Martin-Gay, Beginning Algebra, 5ed 1212

a)

b)

c)

d)

e)