Micah is thinking of a 2-digit number. It is a multiple of 6 and 12. It is a factor of 108. The sum of its digits is 9. What number is Micah thinking of?

So we need to find the common multiples of 6 and 12. Which are basically the multiples of 12, since 6 is always divisible to 12. So (12, 24, 36, 48, 60, 72, 84, 96, 108) Since it is a factor of 108, we stop at 108 (since a number greater than 108 can't be a factor of 108)

Now we find the factors of 108

108 = 1,2,3,4,6,9,12,18,27,36,54,108

The numbers in both lists are 36 and 108 but since Micah is thinking of a 2-digit number, the number she is thinking of is 36.