Answer
LCM = $(x-2)(x+2)(x+1)$
Work Step by Step
Step 1:
Factor each polynomial completely.
$x^{2}-4$ = a difference of squares =$(x-2)(x+2)$
$ x^{2}-x-2 =\quad$ ... we want factors of -2 whose sum is -1
$=(x-2)(x+1)$
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 = $(x-2)(x+2)(x+1)$
