Question

The traffic lights at three different signal points change after every 45 seconds, 75 seconds
and 90 seconds respectively. If all change simultaneously at 7:20:15 hours, then they will change
again simultaneously at?

Answer 1

The 3 signals (at 3 points) change every 45 s, 75 s, 90 s
So, they will change simultaneously for a common time, which is the common multiple or L.C.M of the three
45 = 5*9 = 3^2 * 5
75 = 3*25 = 3 * 5^2
90 = 9*10 = 2* 3^2 * 5
L.C.M(45,75,90) = 2 * 3^2 * 5^2 = 2*9*25 = 450  s
So, they will change simultaneously every 450 s or 7 mins 30 sec
So, next they will change together at 7:27:45 hours.
Hope it helps. 

Answer 2

Answer:

The 3 signals (at 3 points) change every 45 s, 75 s, 90 s

So, they will change simultaneously for a common time, which is the common multiple or L.C.M of the three

45 = 5*9 = 3^2 * 5

75 = 3*25 = 3 * 5^2

90 = 9*10 = 2* 3^2 * 5

L.C.M(45,75,90) = 2 * 3^2 * 5^2 = 2*9*25 = 450  s

So, they will change simultaneously every 450 s or 7 mins 30 sec

So, next they will change together at 7:27:45 hours.

Hope it helps. 

: