Find the smallest number by which 72 must be multiplied, so that the product is

Factorize 72 = 2^3 × 3^2. For a perfect cube, each exponent must be a multiple of 3. The exponent of 3 is 2, so we need one more factor of 3. Multiplying by 3 gives 2^3 × 3^3 = (2×3)^3 = 6^3 = 216, a perfect cube. Thus, the smallest number is 3.