Answer
LCM = $x(x-3)(x+3)$
Work Step by Step
Step 1:
Factor each polynomial completely.
$(x-3)\quad $... is factored
$x^{2}+3x=x(x+3)$
$x^{3}-9x=x(x^{2}-9)$
... recognize a difference of squares
$=x(x-3)(x+3)$
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 = $x(x-3)(x+3)$
