\(\dfrac{x}{3}=\dfrac{y}{2}=\dfrac{z}{5}=k\Rightarrow x=3k,y=2k,z=5k\)
\(xyz=240\Rightarrow30k^3=240\Rightarrow k^3=8\Rightarrow k=2\)
\(\Rightarrow\dfrac{x}{3}=\dfrac{y}{2}=\dfrac{z}{5}=2\)
\(\dfrac{x}{3}=2\Rightarrow x=6\\ \dfrac{y}{2}=2\Rightarrow y=4\\ \dfrac{z}{5}=2\Rightarrow z=10\)