One light flashes every 18 seconds and the other flashes every 12 seconds. If they flash together at 8:00pm, what is the next time that they will flash together?

Ur basically looking for the lowest common multiple ... and it is 36 ... so they will flash together again in 36 seconds ... so its still gonna be 8:00 pm ... just 36 seconds later

What these types of problems want you to find is the least common multiple.

The LCM will be the product of the highest occurring primes of the numbers prime factorization.

12=2*2*3, 18=2*3*3

So the LCM is 2*2*3*3=36

So the lights will flash again at the same time 36 seconds after 8 pm, or if you prefer:

8:00:36