Question

A light flashes every 3 minutes, a second light every 90 seconds, and a third light every 45

seconds. If the three lights flash together at 8:00 AM Monday morning, when is the next time

they will all flash together?

Answer 1

The next time they will all flash together at 8:03 AM.

Explanation:

Given : A light flashes every 3 minutes, a second light every 90 seconds, and a third light every 45 seconds. If the three lights flash together at 8:00 AM Monday morning.

To find : When is the next time they will all flash together?

Solution :

First flashes in 3 minutes.

In seconds, 1 minute = 60 second

3 minute = 180 second

Second in 90 seconds.

Third is 45 second.

To get that light flash together we find the LCM of 45,90 and 180.

2 | 45 90 180

2 | 45 45 90

3 | 45 45 45

3 | 15 15 15

5 | 5 5 5

| 1 1 1

`LCM(45,90,180)=2* 2* 3* 3* 5`

`LCM(45,90,180)=180`

Three lights flash together at 180 second.

Convert into minutes,

1 second =
`(1)/(60)` minutes

180 second =
`(180)/(60)` minutes

180 second = 3 minutes

The three lights flash together after 3 minutes.

Therefore, the next time they will all flash together at 8:03 AM.