Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m. then at what time will they again change simultaneously?

Answer 1

Given: Three traffic lights change every 48 s, 72 s and 108 s and they all change together at 8:00 a.m.

Step-wise calculation:

1. Prime factorise:

48 = 2⁴ × 3

72 = 2³ × 3²

108 = 2² × 3³

2. LCM = `2^max(4, 3, 2) xx 3^max(1, 2, 3)`

= 2⁴ × 3³

= 16 × 27

= 432 seconds

3. Convert:

432 s = 7 minutes 12 seconds

4. Add to 8 : 00 : 00 a.m.: 

8 : 00 : 00 + 7 min 12 s 

= 8 : 07 : 12 a.m.

They will next change simultaneously at 8 : 07 : 12 a.m.