Alocal art studio offers a new session of drawing classes every 12 days. a competing art studio offers a new session of drawing classes every 8 days. today, both art studios have started a new session of drawing classes. in how many days will both art studio start a new drawing session on the same day? show or explain how you know.

To solve this we are going to find the least common multiple of 8 and 12.
Remember that the least common multiple (LCM) of tow or more numbers is the smallest positive number that is multiple of those two or more numbers. 
To find our LCM we are going to list the multiples of 8 and 12, and then, we are going to select the first common number in those lists:

Multiples of 8: 8,16,24,32,40,
Multiples of 12: 12,24,36,48,...

Notice that the first common value between the two list is 24, and that is precisely the number of days it will take for drawing sessions to coincide.

We can conclude that after 24 days both art studios will start a new drawing session on the same day.