The traffic lights at three different signal points change after every 35 s, 45 s and 75 s respectively. If all change simultaneously at 6:20:15 hours, then at what hours will they change again simultaneously?

Correct option is A

Given:

Time intervals for the traffic lights to change: 35 s, 45 s, and 75 s
Initial simultaneous change time: 6:20:15 hours

Formula Used:
LCM (Least Common Multiple) of time intervals = Time after which all signals change simultaneously again
New Time = Initial Time + LCM(seconds)

Solution:
Find LCM of 35, 45, and 75:

Prime factors:

35 = 5 × 7

45 = 3² × 5

75 = 3 × 5²

LCM = 3² × 5² × 7 = 9 × 25 × 7 = 1575 seconds

Convert 1575 seconds to minutes:

1575 ÷ 60 = 26 minutes and 15 seconds

Add to 6:20:15:

6:20:15 + 0:26:15 = 6:46:30