Question

Bill and Sue both work at night. Bill has every sixth night off and Sue has every eighth night off. If they are both off tonight, how many nights will it be before they are both off again?
Ms. Sue
What is the least common multiple?

Mike
I think the LCM is 6...?

Wouldn't it be that they will never have the same day off again because one has a day off every 6 and the other 8th day?
Ms. Sue
These are the days they have off:

6, 12, 18, 24, 30, 36

8, 16, 24, 32, 40


Mike
But the question asks "how many nights will it be before they are both off again" so would the answer be... Bill 6 and Sue 8?

Thanks.
Ms. Sue
The question is asking you how many nights it will be before BOTH are off on the same night.

Check the multiples chart above to see how long it will be. What is the smallest multiple of both numbers?

Mike
Ah... The light just went on... 24!