AMC 12 2002b Problem 19

If $a,b,$ and $c$ are positive real numbers such that $a(b+c) = 152, b(c+a) = 162,$ and $c(a+b) = 170$, then $abc$ is

$\mathrm{(A)}\ 672 \mathrm{(B)}\ 688 \mathrm{(C)}\ 704 \mathrm{(D)}\ 720 \mathrm{(E)}\ 750$