A light flashes every 15 minutes. a second light flashes every 18 minutes. both lights flash together are 2 a.m. What will the time be when they net flash together?
1st light:
15 30 45 90 ...
2nd light:
18 36 54 72 90....
ahhh!!
So what is 90 minutes from 2:00 am ?
another way to look at it ...
What is the LCM for 15 and 18 ?
It's 3:30 am
Well, these two lights seem to have quite the complicated relationship! Let's see if we can figure out when they will next flash together.
First, let's find the least common multiple (LCM) of 15 and 18. The LCM of these numbers is 90. This means that the two lights will flash together every 90 minutes.
Since they flashed together at 2 a.m., we can add 90 minutes to that time. So, the next time they will flash together will be at 3:30 a.m.
But hey, don't be surprised if they decide to change their routine and mess with us again! Those lights sure know how to keep us on our toes!
To determine when the two lights will flash together again, we need to find the least common multiple (LCM) of their flash intervals.
The first light flashes every 15 minutes, so its flash intervals can be predicted by the sequence: 15, 30, 45, 60, 75, 90, 105, 120, 135, etc.
The second light flashes every 18 minutes, so its flash intervals can be predicted by the sequence: 18, 36, 54, 72, 90, 108, 126, etc.
To find the LCM, we can write out both sequences and identify the first number that appears in both lists:
15, 30, 45, 60, 75, 90, 105, 120, 135, ...
18, 36, 54, 72, 90, 108, 126, ...
We can see that they both have a flash interval of 90 minutes. Therefore, the two lights will flash together again in 90 minutes.
Since they flash together at 2 a.m., we can simply add 90 minutes to 2 a.m. to determine the next occurrence:
2:00 a.m. + 1 hour 30 minutes = 3:30 a.m.
Thus, the next time the two lights will flash together is at 3:30 a.m.