Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds. If they change simultaneously at 7 a.m., at what time will they change together next?

Answer 1

Given: Three traffic lights change every 48 s, 72 s and 108 s and they change together at 7:00:00 AM.

Step-wise calculation:

1. Prime factors:

48 = 2⁴ × 3 

72 = 2³ × 3²

108 = 2² × 3³

2. LCM = 2⁴ × 3³

= 16 × 27

= 432 seconds.

3. 432 seconds = 7 minutes 12 seconds.

4. Next simultaneous change = 7:00:00 AM + 7 min 12 s = 7:07:12 AM.