Question

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

Answer 1

Answer:

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

Step-by-step 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

$LCM(45,90,180)=2\times 2\times 3\times 3\times 5$

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

Three lights flash together at 180 second.

Convert into minutes,

1 second = $\frac{1}{60}$ minutes

180 second = $\frac{180}{60}$ 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.