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Todd and Kenneth are shelving books at a public library. Todd shelves 8 books at a time, whereas Kenneth shelves 16 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?

Question

Todd and Kenneth are shelving books at a public library. Todd shelves 8 books at a time, whereas Kenneth shelves 16 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?

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Solution

The smallest number of books each could have shelved is determined by finding the least common multiple (LCM) of the numbers 8 and 16, which represent the number of books Todd and Kenneth can shelve at a time, respectively.

Step 1: List the multiples of each number.

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160...

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160...

Step 2: Identify the least common multiple.

The least common multiple of 8 and 16 is 16.

Therefore, the smallest number of books each could have shelved is 16.

This problem has been solved

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