Karin and Tim are shelving books at a public library. Karin shelves 3 books at a time, whereas Tim shelves 6 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?
The total needs to have both 3 and 6 as factors, 3*4 = 2*6 = 12
To find the smallest number of books each could have shelved, we need to determine the lowest common multiple (LCM) of the numbers 3 and 6.
To find the LCM, we need to list the multiples of each number until we find a common multiple:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 6: 6, 12, 18, 24, ...
From the lists above, we can see that the first common multiple of 3 and 6 is 6. Therefore, the smallest number of books each could have shelved is 6.