Answer
$120x^{2}$
Work Step by Step
Step 1. Factor both denominators.
$\left\{\begin{array}{ll}
15x^{2} & =3\times 5\times x^{2}\\
24x & =8\times 3\times x=2\times 2\times 2\times 3\times x
\end{array}\right.$
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.
None of the three 2's is in the list, add all three
$ List=3,5,x^{2},2,2,2...\qquad$ (list in progress)
3 is already in the list, do not add it to the list.
$x $is already in the list, do not add it to the list.
Step 4. LCD is the product of the listed factors.
$LCD=3\times 5\times 2\times 2\times 2\times x^{2}=120x^{2}$
