Answer
$175x^{2}$
Work Step by Step
Step 1. Factor both denominators.
$\left\{\begin{array}{ll}
25x^{2} & =5\times 5\times x^{2}\\
35x & =5\times 7\times x
\end{array}\right.$
Step 2. List the factors of the first denominator.
$ List=5,5,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.
$5$ is already in the list, do not add it to the list.
$7$ is not in the list,
$ List=5,5,x^{2},7...\qquad$ (list in progress)
$x $is already in the list, do not add it to the list.
Step 4. LCD is the product of the listed factors.
$LCD=5\times 5\times 7\times x^{2}=175x^{2}$