Three lighthouses flash at intervals of 12,45 and x minutes respectively. If all of them flash at the same time at 12 hours interval, find the smallest / largest possible of x.

I have prime factorized the numbers - please advise how to proceed??

12 = 2^2 x 3

45 = 3^2 x 5

12 hours = 720 mins = 2^4 x 3^2 x 5