Answer
$(x+4)(x-4)$
Work Step by Step
Step 1. Factor both denominators.
The first one is already factored,
the second is a difference of squares.
$\left\{\begin{array}{lll}
(x+4) & & \\
x^{2}-16 & =x^{2}-4^{2} & =(x+4)(x-4)
\end{array}\right.$
Step 2. List the factors of the first denominator.
$ List=(x+4),...\qquad$ (list in progress)
Step 3. Add to the list in step 2 any factors of the second denominator that are not yet listed.
$(x+4)$ is already in the list, do not add it.
$(x-4)$ is not in the list, we add it to the list
$List=(x+4),(x-4)$
Step 4. LCD is the product of the listed factors.
$LCD=(x+4)(x-4)$