The first thing you want to do is list numbers that add up to 10. When you get these numbers, ask yourself, "is 12 a multiple of both of these numbers?"

So, list your number pairs that add up to 10.

10 + 0 = 10.

12 is NOT a multiple of both numbers.

9 + 1 = 10.

12 is NOT a multiple of both numbers.

8 + 2 = 10

12 is NOT a multiple of both numbers.

7 + 3 = 10

12 is NOT a multiple of both numbers.

6 + 4 = 10

12 IS a multiple of both numbers.

5 + 5 = 10

12 is NOT a multiple of both numbers.

The number pair that adds up to 10 and has 12 as a multiple is 6 and 4. Now we have to find out if 12 is the LEAST common multiple of these numbers. List the multiples of both numbers until you get a common multiple for both of them. If that common multiple is 12, then the answer is correct.

6: 6, 12.

4: 4, 8, 12.

12 is, in fact, the least common multiple of 6 and 4, and the sum does add up to 10. The numbers 6 and 4 are your correct answer.