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Bobby tutors students in groups of 8. Meanwhile, Polly tutors students in groups of 12. While discussing their work, the tutors realize that they both work with the same total number of students. What is the smallest number of students each can have?

Question

Bobby tutors students in groups of 8. Meanwhile, Polly tutors students in groups of 12. While discussing their work, the tutors realize that they both work with the same total number of students. What is the smallest number of students each can have?

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Solution

To find the smallest number of students each tutor can have, we need to find the least common multiple (LCM) of the two group sizes, 8 and 12.

Step 1: List the multiples of each number. Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104... Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108...

Step 2: Find the smallest multiple that appears in both lists. The smallest multiple that both 8 and 12 share is 24.

So, the smallest number of students each tutor can have is 24.

This problem has been solved

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