Answer
$3(x-3)(x+3)(2x+5)$
Work Step by Step
To find the least common multiple (LCM), we factor the polynomials completely and the LCM is the product of each of these factors raised to the greatest power that occurs in the polynomials. So we have
$$
3x^-27=3(x^2-9)=3(x-3)(x+3), \quad 2x^2 - x - 15=(2x+5)(x-3)
.$$
Thus, the LCM is $3(x-3)(x+3)(2x+5)$.
