I saw a problem the other day that belongs to a class of problems that I have forgotten how to solve (I'm 55). It went like this.. Trains leave a station every 15mins and every 20 mins. The first two leave together at 9.10am. Do any others leave at the same time and when is the next time? The simple way to solve it is just to write down the two sequences... 15mins: 9.10 9.25 9.40 9.55 10.10 etc 20mins: 9.10 9.30 9.50 10.10 etc and note that they match again at 10.10am Clearly that works for this problem but there must be a better way. I just can't seem to figure out how to do the general case. For example you could assume there is a match at some time ΔT after 9.10 then write... ΔT = n*15 = m*20 where n and m are unknown integers. But thats one equation with two unknowns. I half remember that ΔT must be a multiple of |n-m| or something like that but I think that just adds another unknown integer to the mix.