# Pairwise Products

Algebra Level 2

$\large xy = 24 \quad xz = 30 \quad yz = 15$

If $$x,y,z$$ are positive, then $$x + y + z$$ can be written as $$\frac{a\sqrt{b}}{c}$$, where $$a,b$$ and $$c$$ are positive integers, with $$a$$ and $$c$$ are relatively prime, and $$b$$ is square-free. Find $$a+b+c$$.

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