What are two numbers whose least common multiple is 36 and greatest common factor is 3?

The least common multiple is number n multiplied by number m divided by their greatest common factor.

The prime factors of 36 are 2, 2, 3, and 3.

The two numbers share a factor of 3. The remaining prime factors are 2, 2, and 3. So, if we multiply 3 by 2 x 2 and 3 by 3, we have the pair of numbers 12 and 9. Or, if we multiply 3 by 2 x 2 x 3 and 3 by 1, we have the pair of numbers 36 and 3.

Note: We cannot split the two 2s, because then each number would have 2 as a factor, which would change the greatest common factor to 6.

Our possible two numbers:

9 and 12

3 and 36