Question

The museum performers shows in every schools every Monday and in public LiBraries every 5th day (on both weekends and weekdays). If the museum did both a school show and LiBrary show on Monday, how many days will it be until it does both shows on the same day again?

Answer 1

To determine when the museum will perform at both the school and the library on the same day again, we calculate the least common multiple of 7 (days between school shows) and 5 (days between library shows), which is 35 days.

Step-by-step explanation:

The student is asking a question that involves finding the least common multiple (LCM) of two numbers: the number of days between school shows (7 days, since it's every Monday) and the number of days between library shows (5 days). To find out how many days will pass before both events coincide on the same day again, we need to calculate the LCM of 7 and 5.

Steps to Find the LCM of 7 and 5

1. List the multiples of each number:
   Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
   Multiples of 7: 7, 14, 21, 28, 35, 42, 49, ...
2. Identify the smallest multiple that the two lists share, which in this case is 35.
3. 35 is the least common multiple of 7 and 5.

Therefore, it will be 35 days until the museum performers show up at both schools and libraries on the same day again.