Math Question please help

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

This is a question about the lowest common multiple, or LCM, of 3 minutes, 90 seconds, and 45 seconds. Why? Well, because the amount of time that passes before the light flashes will always be a multiple of 3 minutes, 90 seconds, or 45 seconds. For example:

The 45 second light will flash 45 seconds after 8:00, 90 seconds after, 135 seconds after...

The 90 second light will flash 90 seconds after 8:00, 180 seconds after, 270 seconds after...

The 3 minute light will flash at 8:03, 8:06, 8:09...

We're adding the same unit of time each time- and adding the same number to itself over and over is just multiplication.

To predict when each individual light will flash, we can list out their multiples. The next time that they will flash together will be the smallest multiple they have in common- the lowest common multiple.

First, convert 3 minutes into seconds. 3x60=180 seconds

Then list multiples. 45x1, 45x2, 45x3, 45x4....

Multiples of 45: 45, 90, 135, 180...

Multiples of 90: 90, 180,

Multiples of 180: 180—

Stop! That's it. All three lights will flash 180 seconds, or 3 minutes, after. The LCM of 45, 90, and 180 is 180.

The lights will all flash together at 8:03 AM.

Answer 2

First one flashes every 180 seconds.

Basically you have to find the lowest common multiple of 180, 90, 45. After that number of seconds after 8 am, they will all flash together.

Mike