light X flashes every 3 minutes. Light Y flashes every 5 minutes. Light Z flashes every 7 minutes. At exactly 7:28 AM they all flash together. At what time will they do so again?

a) 9:13
b) 9:15
c) 9:00
d) 9:28

The next time must be a multiple of 3, 5 and 7.

In other words they will flash together 05 minutes from now
or 7 hours, 28 minutes + 105 minutes
= 7 hours, 133 minutes
= 7 hours + 2 hours + 13 minutes

That would make it 9:13

To find out when the lights will flash together again, we need to find the least common multiple (LCM) of 3, 5, and 7. The LCM is the smallest number that is divisible by all three numbers.

To find the LCM, we can start by listing the multiples of each number:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, 42, ...

We can see that the smallest number that is divisible by all three numbers is 105, since it is both a multiple of 3, 5, and 7. Therefore, the lights will flash together again after 105 minutes.

To calculate the time, we need to convert 105 minutes to hours and minutes. Since there are 60 minutes in one hour, we divide 105 by 60 to get the whole number of hours:

105 ÷ 60 = 1 hour and 45 minutes

Adding 1 hour and 45 minutes to the original time of 7:28 AM gives us 9:13 AM. Therefore, the lights will flash together again at 9:13 AM.

So the correct answer is:
a) 9:13