Question

A bag contains equal numbers of green and blue marbles. You can divide all the green marbles in groups of 12 and all the blue marbles into groups of 16. What is the least number of each color made that can be in the bag?

Answer 1

48 of each color.

Explanation:

To determine the smallest possible number of green and blue marbles that can be in the bag, you should find the least common multiple (LCM) of 12 (for the green marbles) and 16 (for the blue marbles).

The LCM is the smallest number that both 12 and 16 can evenly divide into. You can calculate it like this:

Prime factorization of 12: 2^2 * 3

Prime factorization of 16: 2^4

To find the LCM, choose the highest power of each prime factor that is present in either number:

LCM = 2^4 * 3 = 16 * 3 = 48

So, the minimum number of both green and blue marbles in the bag should be 48 each.