three different lights flash every 5 seconds, 8 seconds and 12 seconds respectively. if they start at the same time how long will it take for them to flash at the same time again?

common multiple

5
2*2*2
2*2*3
need
5 2 2 2 3
120

three different lights flash every 8 seconds every 5 seconds and every 12 seconds

What is answer

To determine when the three lights will flash at the same time again, we need to find the least common multiple (LCM) of the three flash intervals.

The flash intervals are 5 seconds, 8 seconds, and 12 seconds.

First, let's list the multiples of each interval until we find a common multiple:

Multiples of 5 seconds: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...

Multiples of 8 seconds: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ...

Multiples of 12 seconds: 12, 24, 36, 48, 60, 72, 84, 96, ...

As we can see, the first common multiple is 24 seconds. This means that after 24 seconds, all three lights will flash simultaneously.

To find when they will flash at the same time again, we need to find the next common multiple.

The multiples of 24 seconds are: 24, 48, 72, 96, ...

Therefore, after 48 seconds, the three lights will flash at the same time again.

So, it will take 48 seconds for the three lights to flash at the same time again.