I'm thinking of two numbers, 12 and another number. 12 and my other number have a greatest common factor of 6 and their least common multiple is 36. What's the other number I'm thinking of?

The product of two numbers and the product of their greatest common factor and least common multiple are always equal.

Let the other number = X.

Greatest common factor is 6

Least common multiple is 36

We now have 6 * 36 = 12 * x

Simplify:

216 = 12x

Divide both sides by 12:

x = 216 / 12

x = 18

The other number is 18.

Number 18 is the number you should be thinking of