Class 6A and class 6B students are gathering to select the numbers of best athletes to honor with an award. Class 6A selects athletes in groups of 3 while class 6B selects athletes in groups of 6. If both classes end up with the same number of athletes, what is the smallest number of athletes each must have selected?

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Solution

We need to find out the smallest number that is a multiple of both 3 and 6. This is the least common multiple.

List the multiples of each number. Find the smallest number that appears in both lists.

Multiples of 3: 3, 6, 9, 12, 15

Multiples of 6: 6, 12, 18, 24, 30

The least common multiple of 3 and 6 is 6. That means that the smallest number of athletes each classes must have selected is 6, because 2 groups of 3 from class 6A is 6 athletes in total and 1 group of 6 from class 6B is 6 athletes in total.

The smallest number of athletes each classes must have selected is 6.

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