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The drama club meets in the school auditorium every 7 days, and the choir meets there every 9 days. If the groups are both meeting in the auditorium today, then how many days from now will they next have to share the auditorium?

Question

The drama club meets in the school auditorium every 7 days, and the choir meets there every 9 days. If the groups are both meeting in the auditorium today, then how many days from now will they next have to share the auditorium?

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Solution

To find out when the drama club and the choir will next share the auditorium, we need to find the least common multiple (LCM) of 7 and 9. The LCM of two numbers is the smallest number that is a multiple of both numbers.

Here are the steps to find the LCM of 7 and 9:

  1. List the multiples of each number:

    Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140...

    Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180...

  2. Find the smallest number that appears in both lists:

    The smallest number that appears in both lists is 63.

So, the drama club and the choir will next have to share the auditorium 63 days from now.

This problem has been solved

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