Three lighthouses flash their light out at intervals of 54,60 and 72 seconds. If they flash together at 20.00 hours,when will they not flash together?

Question

Under H.C.F or L.C.M

Answer 1

54=2*3^3; 60=2^2*3*5; 72=2^3*3^2.

If we produce a set of factors that includes all these we get 2, 2, 2, 3, 3, 3, 5. Multiply these factors together: 1080. So after 1080 seconds lighthouse 1 would flash 20 times, lighthouse 2 18 times, lighthouse 3 15 times.

Answer 2

Note: 20.00hrs is not when they first flash together. They was a conditional statement 'if'. They choose 20.00hrs as the reference point. In order to know when they will next flash together after 20.00hrs, you have to know when they first flash together which is the lowest common multiple of( LCM) of 54, 60 and 72= 1080s= 0.3hr The second, third and subsequent flashing will be in the multiple of 1080. But since 20.00hr is our reference point, it will be 20+0.3 for the next simultaneouse flashes and 20+0.3(2) for the next and so on For this question, the answer is 20.00hr + 0.3hr = 20.3 hrs