Cody and Kiera are shelving books at a public library. Cody shelves 11 books at a time, whereas Kiera shelves 4 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
Cody and Kiera are shelving books at a public library. Cody shelves 11 books at a time, whereas Kiera shelves 4 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?
Solution
The smallest number of books each could have shelved is determined by finding the least common multiple (LCM) of the numbers 11 and 4.
Step 1: List the multiples of each number.
Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220...
Step 2: Find the smallest number that appears in both lists.
The smallest number that appears in both lists is 44.
So, the smallest number of books each could have shelved is 44.
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