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The $L.C.M$ of $\left (x^{3}-x^{2}-2x \right)$ and $\left (x^{3}+x^{2} \right)$ is : 

  1. $\left (x^{3}-x^{2}-2x \right)$
  2. $\left (x^{2}+x \right)$
  3. $\left (x^{4}-x^{3}-2x^{2} \right)$
  4. $x-2$
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Answer is C.

To find the LCM, we have to find all the factors of both the terms.

$x^{3}-x^{^{2}}-2x = x(x^{2}-x-2)$

1st term factors are $x(x-2)(x+1)$

2nd term factors are $x^{3}+x^{2} = x^{2}(x+1)$

So LCM is $x^{2}(x+1)$$(x-2)$ = $x^{2}$($x^{2}-x-2$) = $x^{4}-x^{3} -2x^{2}$
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