What is the LCM of ${(x + 2)}^{2} (x - 2)$ and $(x^{2} - 4 x - 12)$

(x + 2) (x - 2)

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{(x + 2)}^{2} (x - 2) (x - 6)

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(x + 2) {(x - 2)}^{2}

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{(x - 2)}^{2} (x - 2) (x - 6)

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Solution

The correct option is B ${(x + 2)}^{2} (x - 2) (x - 6)$
$(x^{2} - 4 x - 12) = x^{2} - 6 x + 2 x - 12 = (x - 6) (x + 2)$
$∴$ LCM of $(x + 2)^{2} (x - 2) 6 (x - 6) (x + 2)$
is $(x + 2)^{2} (x - 2) (x - 6)$

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