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.