Question

The traffic lights at three different road crossings change after every 48 seconds 72 seconds and 108 seconds respectivily.If they changed simultaneously at 7:00 am.,at what time will they change simultaneously again

Answer 1

Answer:

07:43: 12 AM

Step-by-step explanation:

Given that:

Traffic lights change after every 48, 72 and 108 seconds.

They changed simultaneously at 7:00 AM.

To find:

At what time, they will change simultaneously again ?

Solution:

For this, we need to find LCM(Least Common Multiple) of the three numbers and then add it to 7:00 AM to find the time they will change together again.

Because LCM of 3 numbers is the least number which is divisible by all 3 numbers.

Let us factorize the numbers and underline the common part:

$48 = \underline{12}\times 4\\72 = \underline{12}\times 6\\108 = \underline{12}\times 9$

Common part is taken only once and the remaining part is multiplied to it to find the LCM.

So, LCM = $12 \times 4\times 6 \times 9 = 2592$

In 2592 seconds, they will change together again.

Changing 2592 seconds in minutes:

Let us divide it by 60:

We get 43 minutes 12 seconds.

Let us add it to 7:00AM, we get the following:

So, the time at which they will change simultaneously = 07:43: 12 AM