Answer
$(y-4)^{2}(y+4)$
Work Step by Step
We are given the denominators $y^{2}-16$ and $y^{2}-8y+16$.
In order to find the least common denominator, we must factor each denominator.
$y^{2}-16=(y+4)(y-4)$
$y^{2}-8y+16=(y-4)(y-4)=(y-4)^{2}$
Next, we multiply together all distinct factors from each denominator, with each factor raised to the greatest power that occurs in any denominator.
$LCD=(y-4)^{2}\times(y+4)=(y-4)^{2}(y+4)$
