The traffic lights at three different signal points change after every 45 seconds 75 seconds and 90 ...........

Quantitative Aptitiude (CLAT) LCM, HCF

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

7:27:30 hours

7:28:00 hours

7:27:50 hours

7:27:45 hours

Explanation:

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.