Answer
$y(y+7)(y-7)$
Work Step by Step
Step 1. Factor both denominators.
The first one is a difference of squares,
the second is already factored.
$\left\{\begin{array}{lll}
y^{2}-49 & =y^{2}-7^{2} & =(y+7)(y-7)\\
y(y-7) & &
\end{array}\right.$
Step 2. List the factors of the first denominator.
$ List=(y+7),(y-7),...\qquad$ (list in progress)
Step 3. Add to the list in step 2 any factors of the second denominator that are not yet listed.
$y$ is not in the list, we add it to the list
$List=(y+7),(y-7),y,...$
$(y-7)$ is already in the list, do not add it.
Step 4. LCD is the product of the listed factors.
$LCD=y(y+7)(y-7)$
