# Find the LCM of the given polynomial. x^{3}-x, x^{2}-x

Find the LCM of the given polynomial.
${x}^{3}-x,{x}^{2}-x$
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Step 1
To find the LCM of given polynomial: ${x}^{3}-x,{x}^{2}-x$.
Solution:
${x}^{3}-x=x\left({x}^{2}-1\right)$
$⇒{x}^{3}-x=x\left(x+1\right)\left(x-1\right)$ (using, $\left({a}^{2}-{b}^{2}\right)=\left(a+b\right)\left(a-b\right)$)
$⇒{x}^{3}-x=x\left(x+1\right)\left(x-1\right)$...(1)
And,
${x}^{2}-x=x\left(x-1\right)$...(2)
Using,(1) and (2) LCM of ${x}^{3}-x,{x}^{2}-x$ is given by:
x(x+1)(x-1).
Step 2
Result:
LCM is: x(x+1)(x-1).