Answer
LCM = $(x-4)^{2}(x+3)$
Work Step by Step
Step 1:
Factor each polynomial completely.
For $x^{2}+bx+c$,
we search for factors of c whose sum is b:
$x^{2}-x-12...\qquad $...-4 and +3
$=(x-4)(x+3)$
$x^{2}-8x+16=...\qquad $...-4 and -4
$=(x-4)^{2}$
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 = $(x-4)^{2}(x+3)$
