Answer
$(x+10)(x-10)^2$
Work Step by Step
Step 1. Factor each denominator completely
$x^2-100=(x+10)(x-10)$ and $x^2-20x+100=(x-10)^2=(x-10)(x-10)$
Step 2. List all the factors of the first denominator
$(x+10), (x-10)$
Step 3. Add to the list any additional factors in the second denominator; we need to add $(x-10)$ to the list.
Step 4. The least common denominator is
$LCD=(x+10)(x-10)(x-10)=(x+10)(x-10)^2$
