Answer
$120x^{5}$
Work Step by Step
Step 1. Factor both denominators.
$\left\{\begin{array}{ll}
15x^{2} & =3\times 5\times x^{2}\\
24x^{5} & =8\times 3\times x^{5}=2\times 2\times 2\times 3\times x\times x\times x\times x\times x
\end{array}\right.$
Step 2. List the factors of the first denominator.
$ List=3,5,x^{2}...\qquad$ (list in progress)
Step 3. Add to the list in step 2 any factors of the second denominator that are not yet listed.
$2$ is not in the list, we add all three 2's to the list
$ List=3,5,x^{2},2^{3}...\qquad$ (list in progress)
$3$ is already in the list, do not add it to the list.
Two of the five x's are already in the list, we add the other three to the list.
$List=3,5,x^{2},2^{3}, x^{3}$
Step 4. LCD is the product of the listed factors.
$LCD=3\times 5\times 2^{3}\times x^{2}\times x^{3}=120x^{5}$
