Answer
LCM = $3(x-3)(x+3)(2x+5)$
Work Step by Step
Step 1:
Factor each polynomial completely.
$3x^{2}-27=3(x^{2}-9)$... recognize a difference of squares
$=3(x-3)(x+3)$
$2x^{2}-x-15=...$
For $ax^{2}+bx+c$
we search for factors of ac whose sum is b,
and rewrite the $bx$ term.
$-6$ and $+5$ are such factors,
$2x^{2}-x-15=2x^{2}-6x+5x-15=$
$=2x(x-3)+5(x-3)$
$=(2x+5)(x-3)$
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 = $3(x-3)(x+3)(2x+5)$
