What is the LCM of x3 8 x2 5x 6 and x3 4x2 4x ........

Quantitative Aptitude (CDS) Algebra

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What is the LCM of x³ +8 , x² + 5x + 6 and x³ + 4x² + 4x ?

x(x+2)²(x+3)(x²-2x+4)

x(x-2)²(x-3)(x²+2x+4)

(x+2)²(x+3)(x²-2x+4)

(x-2)²(x-3)(x²-2x+4)

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Explanation:

As x³+8
=x³+2³
=(x+2)(x²-2x+4)------------------------------(i)
x²+5x+6
=(x+2)(x+3)-----------------------------------(ii)
x³+4x²+4x
x(x²+4x+4)
x(x+2)²-------------------------------------------(iii)
From (i), (ii) and (iii)
LCM=x(x+2)²(x+3)(x²-2x+4)