Question

Traffic lights at three different road crossing change after 48 sec,72sec and 108 sec respectively. At what time will they change together again if they change simultaneously at 7 A.M.? (with full statement )please answer the questions

Answer 1

Given that traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.
48 = 2 × 2 × 2 × 2 × 3
72 = 2 × 2 × 2 × 3 × 3
108 = 2 × 2 × 3 × 3 × 3
Hence LCM of 48, 72 and 108 is (2 × 2 × 2 × 2 × 3 × 3 × 3)
= 432
That is after 432 seconds they will change simultaneously
432 seconds = 7 min 12 seconds
Thus the traffic lights change simultaneously at 7:7:12 am

Answer 2

The LCM of 48, 72, 108 will be the time after the lights change
48 = 2^4*3
72 = 2^3*3^2
108 = 2^2*3^3
LCM = 2^4*3^3
LCM = 432

The lights will change together after 432 second = 7 mins 12 secs
Time at which light will change together = 7:7:12