Question

You and your brother both work the​ 4:00 P.M. to midnight shift. You have every ninth night off. Your brother has every sixth

night off. Both of you were off on 1. Your brother would like to see a movie with you. When will the two of you have the same night off​ again?

Answer 1

The siblings will both have the night off again on the 18th night after the given date, as the Least Common Multiple (LCM) of 9 and 6 is 18.

Step-by-step explanation:

The question asks when two siblings, one with a day off every ninth night and the other every sixth night, will both have a night off again if they both last had the same night off on a given date. This is a Least Common Multiple (LCM) problem, which can be solved by finding the smallest number that is a multiple of both 9 and 6. The multiples of 9 are 9, 18, 27, 36, and so on. The multiples of 6 are 6, 12, 18, 24, 30, 36, and so on. The first common multiple of both 9 and 6 is 18. So, the next time they will both have a night off is on the 18th night after the given date.