If a red light flashes every 3 seconds, a blue light flashes every 4 seconds and a blue light flashes every 5 seconds and they all flashed together at midnight when would be the next time they all flash together?
What is the least common multiple of 3, 4, and 5?
In an hour
To determine when the lights will flash together again, we need to find the least common multiple (LCM) of the three flashing intervals: 3 seconds, 4 seconds, and 5 seconds.
One way to find the LCM is by listing the multiples of each number until we find a common multiple. Let's start with the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, ...
Next, let's list the multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, ...
Finally, let's list the multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
From the lists above, we can see that the next time the three lights flash together after midnight is after 60 seconds, which is their least common multiple. Therefore, they will flash together again one minute after midnight.
If you're looking for a specific time, you can add the found LCM of 60 seconds to the initial time of midnight. So, the next time the lights will all flash together after midnight is at 12:01 AM.