In a three-digit number, the hundreds digit is greater than 5, the tens digit is greater than 4 but less than 8, and the units digit is the smallest prime number. How many three-digit numbers satisfy all of these conditions?

The hundreds digit can be 6, 7, 8, 9.

The tens digit can be 5, 6, 7.

The units digit is 2.

There are 4 possible digits for the hundreds digit, 3 possible digits for the tens digit, and 1 digit for the ones digit.

The total number of numbers is

4 * 3 * 1 = 12

Answer: 12