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?
What is the least common multiple?
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?
These are the days they have off:
6, 12, 18, 24, 30, 36
8, 16, 24, 32, 40
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.
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?
Ah... The light just went on... 24!
To find out how many nights it will be before Bill and Sue are both off again, we need to find the smallest common multiple of 6 and 8.
One way to find the common multiple is by listing the multiples of each number until we find one they both share:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, ...
From the list, we see that the first common multiple of 6 and 8 is 24.
Therefore, it will be 24 nights before Bill and Sue are both off again.