Question

One sign lights up every 10 seconds. One sign lights up every 12 seconds. If they have just lit up at the same time, how many seconds will it take for the signs to light up at the same time again?

Answer 1

It will take 60 seconds for the signs to light up at the same time again.

Explanation:

Given:

One sign lights up every 10 seconds

One sign lights up every 12 seconds

They have just lit up at the same time.

To find in how many seconds will it take for the signs to light up at the same time again.

Solution:

In order to find the time in seconds will it take for the signs to light up at the same time again, we need to find the least common multiple of the the times for which the given signs light up.

The numbers are 10 and 12.

To find the LCM, we will list the multiples of each and check the least common multiple.

The multiples of 10 and 12 are :

`10\rightarrow 10,20,30,40,50,60,70`

`12\rightarrow 12,24,36,48,60`

thus, we can see that 60 is the least common multiple.

Thus, the signs will light up at the same time time after every 60 seconds.