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LCM

The LCM of ...

Question

The LCM of $6 (x^{2} + x y), 8 (x y - y^{2}), 12 (x^{2} - y^{2}) a n d 20 {(x + y)}^{2}$ is

A

120 x (x + y) (x - y)

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B

120 x y (x + y) (x - y)

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C

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

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D

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

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Solution

The correct option is C $120 x y {(x + y)}^{2} (x - y)$
$6 (x^{2} + x y) = 6 x (x + y)$
$8 (x y - y^{2}) = 8 y (x - y)$
$12 (x^{2} - y^{2}) = 12 (x - y) (x + y)$
$20 {(x + y)}^{2} = 20 (x + y) (x + y)$
LCM of 6, 8, 12, 20 = 120
$∴$ Reqd LCM = $120 x y (x - y) {(x + y)}^{2}$

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