smc

Adding up the three equations gives $2(ab+bc+ca)=152+162+170=484⟹ab+bc+ca=242$. Subtracting each of the above equations from this yields, respectively, $bc=90,ca=80,ab=72$. Taking their product, $ab\cdot bc\cdot ca=a^2{b}^2{c}^2=90\cdot 80\cdot 72=720^2⟹abc=\boxed{720}\Rightarrow (\mathrm{D})$.