Work out the volume of the prism below. Give your answer in $\mathrm{cm}^{3}$.

Step 1 ：Let the dimensions of the rectangular prism be x, y, and z, such that xy = 30, yz = 180, and zx = 24.

Step 2 ：Multiply all three equations together: xy * yz * zx = (xyz)^2 = 30 * 180 * 24.

Step 3 ：Find the prime factorization of the right-hand side: (2 * 3 * 5) * (2^2 * 3^2 * 5) * (2^3 * 3) = 2^6 * 3^4 * 5^2.

Step 4 ：Thus, (xyz)^2 = (2^3 * 3^2 * 5)^2, so xyz = \(\boxed{360}\) cm^3.