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)$ = $x^{2}$($x^{2}-x-2$) = $x^{4}-x^{3} -2x^{2}$