Answer
LCM = $x(x-1)(x+1)$
Work Step by Step
Step 1:
Factor each polynomial completely.
$x^{3}-x=x(x^{2}-1)=$ ... recognize a difference of squares
$=x(x-1)(x+1)$
$x^{2}-x=x(x-1)$
Step 2:
The LCM is the product of each of these factors raised to a power equal to the greatest number of times that the factor occurs in the polynomials.
LCM = $x(x-1)(x+1)$
