The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively - Maths - Playing with Numbers

Question

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

Gopal Mohanty · Accepted Answer

Time period after which these lights will change = LCM of 48,
72, 108

2

48, 72, 108

2

24, 36, 54

2

12, 18, 27

2

6, 9, 27

3

3, 9, 27

3

1, 3, 9

3

1, 1, 3

1, 1, 1

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 =
432
They will change together after every 432 seconds i e , 7 min 12
seconds
Hence, they will change simultaneously at 7:07:12 am

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