What is the smallest positive integer with factors of 16, 15, and 12?
We are asked to find the least common multiple of 16, 15, and 12.  Prime factorizing these three numbers as $2^4$, $3\cdot5$, and $2^2\cdot 3$, we find that a common multiple must have at least four twos, one three, and one five in its prime factorization.  Therefore, the least common multiple is $2^4\cdot3\cdot5=\boxed{240}$.