# The sum of two numbers is 10 and their lcm is 12. How do I find the numbers?

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?"

• 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.

thanked the writer. 