### Instruction: What is the smallest positive integer with factors of 16, 15, and 12?### Response: I need to find a number that is a multiple of 16, 15, and 12.
One way to do this is to find the least common multiple of these three numbers.
To find the least common multiple, I can use prime factorization.
I can write each number as a product of prime factors: 16 = 2^4, 15 = 3 * 5, and 12 = 2^2 * 3.
The least common multiple will have each prime factor raised to the highest power that appears in any of the three numbers.
So the least common multiple is 2^4 * 3 * 5, which is 240.
Therefore, the smallest positive integer with factors of 16, 15, and 12 is 240.