Correct Answer - Option 2 : 10:18:36 AM
Given:
Traffic lights at 3 road crossings change after 24, 36 and 54 seconds respectively.
Time of changing of traffic lights for the first time = 10:15:00 AM
Concept:
LCM = Lowest Common Multiple is the common multiple of two or more numbers that is the lowest possible number that is divisible by those numbers.
Calculation:
The time when traffic lights again change simultaneously will be the LCM of 24 seconds, 36 seconds and 54 seconds respectively.
⇒ LCM (24, 36, 54) can be calculated by prime factorization.
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
54 = 2 × 3 × 3 × 3
LCM (24, 36, 54) = 2 × 2 × 2 × 3 × 3 × 3
⇒ 216 seconds
The three traffic lights at different road crossings will change after 216 seconds.
∴ The next time of changing of lights will be at 10:15:00 AM + 216 seconds
⇒ 10:15:00 AM + 216/60 minutes
⇒ 10:15:00 AM + 3 minutes + 36 seconds
⇒ 10:18:36 AM
