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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
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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
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a)
b)
c)
d)
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