# 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?

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Updated on: September 25th, 2023

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., the lights change simultaneously again at 7:07:12 am.

Traffic lights at three different road crossings change after every 48 seconds, 72 seconds, and 108 seconds. We have to find at what time the three signals change together again. The three lights change simultaneously on the common multiples of all three. Therefore, we have to find the LCM of 48, 72, and 108.

## Time when Traffic lights change simultaneously

At three different road crossings, the traffic light changes every 48 seconds, 72 seconds, and 108 seconds, accordingly. So, let’s take LCM of 48, 72 and 108.

Solution

By taking LCM of the numbers

48 = 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

108 = 2 x 2 x 3 x 3 x 3

LCM of 48, 72 and 108 = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 432

After 432 seconds, traffic lights change simultaneously

As 60 seconds = 1 minute

By dividing 432 by 60, we get 12 as the remainder and 7 as the quotient

432 seconds = 7 min 12 seconds

Time = 7 am + 7 minutes 12 seconds

Therefore, the lights change simultaneously again at 7:07:12 am.

Summary

## 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?

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. The lights change simultaneously again at 7:07:12 am.

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