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The Chess club and the Robotics team both meet in the school gym. The chess club meets every six days. The Robotics team meets every eight days They are sharing the gym today. In how many days will they share the gym again?

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Answer: 24 days

Explanation:

The number of days from now when the chess club will be in the gym:

6, 12, 18, 24, 30, 36, ...

The number of days from now when the robotics team will be there:

8, 16, 24, 32, 40, 48, ...

The lowest number they have in common is 24 days.

A more algebraic way to look at this (which is what your instructor probably wants) is to find the smallest whole number that is divisible by 6 and also divisible by 8.

The prime factorization of 6 is 2*3

The prime factorization of 8 is 2*2*2

The smallest whole number divisible by 6 and by 8 must have all the prime factors but no more than that.

For the factor of 2, the number 6 has one of them and 8 has three of them , so we need the highest number of factors for just one of the numbers --> 3 factors of 2 (We don't add the 3 factors from 8 and the one factor from 6 to get 4 factors. That would be incorrect.)

For the factor of 3, it only appears as a factor of 6 and it only appears once --> one factor of 3.

So, we need 2 * 2 * 2 * 3 = 24

I hope this helps.

User Tazo Leladze
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