Question

A librarian restocks books every 12 days and magazines every 18 days. How often does she restock both on the same day?(1 point

Answer 1

To find out how often the librarian restocks both books and magazines on the same day, we need to calculate the least common multiple (LCM) of the two restocking periods: 12 days and 18 days.

First, we can find the prime factorization of each number:

- \(12 = 2^2 \times 3^1\)
- \(18 = 2^1 \times 3^2\)

Next, we take the highest power of each prime factor from both factorizations:

- For the prime number 2, the highest power is \(2^2\).
- For the prime number 3, the highest power is \(3^2\).

Now we calculate the LCM:

\[
\text{LCM} = 2^2 \times 3^2 = 4 \times 9 = 36
\]

Thus, the librarian will restock both books and magazines on the same day every **36 days**.