The product of the three digits of a 3-digit number is 12. How many such numbers are there?

No digit can be 0. Digit sets with product 12: {1, 2, 6} and {1, 3, 4} give $3!=6$ numbers each; {2, 2, 3} gives $\frac{3!}{2!}=3$. Total $6+6+3=15$. (12 misses the repeated-digit set {2, 2, 3}.)