Question

Exit ticket: Joehamster eats 12 muffin morsels every sixth day, 24 celery sticks every 8th oday, and 18 cookies every 10th day. After how many days will he eat all three food items on the same day?

Answer 1

In order to calculate after how many days all three food items will be eaten in the same day, we need to calculate the least common multiple (LCM) between the periods of 6 days, 8 days and 10 days.

First, let's factorize each number:

`\begin{gathered} 6\to2\cdot3 \\ 8\to2\cdot2\cdot2 \\ 10\to2\cdot5 \end{gathered}`

Then, let's multiply the factors using the maximum number of time they appear in a number, that is, number 2 three times, number 3 one time and number 5 one time:

`2\cdot2\cdot2\cdot3\cdot5=120`

So after 120 days all three food items will be eaten on the same day.