Ronald and Tim both did their laundry today. Ronald does laundry every 666 days and Tim does laundry every 999 days.

How many days will it be until Ronald and Tim both do laundry on the same day again?

It will be 18 days.

We want the least common multiple (LCM) of 6 and 9. First we find the prime factorization:

6 = 2*3

9 = 3*3

They have a 3 in common; we use this first in the LCM. Then we take the "leftover" factors, 2 and 3:

LCM = 3*2*3 = 18