Question

Logan and Nathan are shelving books at a public library. Logan shelves 5 books at a time, whereas Nathan shelves 6 books at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?

Answer 1

The smallest number of books each Logan and Nathan could have shelved is 30.

Step-by-step explanation:

To find the smallest number of books each Logan and Nathan could have shelved, we need to find a common multiple of 5 and 6. The common multiple represents the number of books both of them would have to shelve in order to have the same number. The common multiple of 5 and 6 is 30. Therefore, the smallest number of books each Logan and Nathan could have shelved is 30.

Answer 2

30

Step-by-step explanation:

Given that

Logan shelves 5 books and

Nathan shelves 6 books

They end shelving the same number of books.

To find:

Smallest number of books each could have shelved?

Solution:

First of all, let us have a look at the definition of Least Common Multiple(LCM) of two numbers.

Least Common Multiple (LCM) of two numbers is the minimum number which is divisible by both the numbers.

Now, looking at the statement of the given question.

We have to find the LCM of both the numbers actually.

Making factors of the numbers:

`5=5* 1`

`6=2* 3`

Nothing is common here, therefore the LCM is
`5* 6 =\bold{30}`.

Smallest number of books shelved = 30