Question

The least common multiple of two whole numbers is 12. The ratio of the

greater number to the lesser number is 3 : 2. What are the two numbers?

Answer 1

9514 1404 393

Answer:

6 : 4

Explanation:

The product of the ratio values is 3×2 = 6. This means the two numbers will have a GCF of 12/6 = 2. So, the two numbers are ...

3×2 : 2×2 = 6 : 4

_____

I think of GCF and LCM problems in terms of a "diagram" that looks like this:

(a [ b ) c ]

That is, the two numbers can be written in a form such that one is (a·b), the other is [b·c], their greatest common factor is b, and their least common multiple is a·b·c.

The ratio of the two numbers would be a : c. The product ac differs from the LCM by a factor of b, the GCF. Of course, b = abc/(ac), which is how we got the above answer.