MathematicsOn GT road, three consecutive traffic lights change after 36, 42, and 72 seconds. If the lights are first switched on at 9:00am , then at what time will they change simultaneously?

On GT road, three consecutive traffic lights change after 36, 42, and $72$ seconds. If the lights are first switched on at $9 : 00 am$ , then at what time will they change simultaneously?

A
9:08:24 am
B
9:00:72 am
C
9:02:30 am
D
9:08:24 pm

Solution:

It is given that the traffic lights change after 36, 42, and 72 seconds and they are first switched on at 9:00 AM.
Time after which light change simultaneously = LCM of all the three intervals
Prime Factorization of the numbers:

LCM of 36, 42, and 72 = 504 seconds
Converting seconds into minutes
60 seconds = 1 minute
⇒ 504 sec = 8 min 24 sec
Then the time at which the lights will switch on simultaneously
⇒ 9:00:00 + 00:08:24
⇒ 9:08:24 AM
Hence, the traffic lights change simultaneously at 9:08:24 AM.
Hence, the correct option is 1.