Two lights flash every 15 and 45 seconds respectively.If the two lights flashed together at 3 p.m.,at what time will they flash together next time?
Very simple, since the LCM of 15 and 45 is 45, they will flash in unison every 45 seconds, so add 45 sec to 3 pm or
3:00:45 pm
This answer is very very tati
To determine the time at which the two lights will flash together next, we need to find the lowest common multiple (LCM) of 15 seconds and 45 seconds. The LCM is the smallest multiple that is divisible by both numbers.
To find the LCM of 15 and 45, you can follow these steps:
Step 1: Write down the prime factorization of each number.
15 = 3 * 5
45 = 3 * 3 * 5
Step 2: Take the highest power of each prime factor appearing in the factorizations.
The highest power of 3 is 3^2 (from 45).
The highest power of 5 is just 5 (from both 15 and 45).
Step 3: Multiply the highest powers of each prime factor together.
3^2 * 5 = 9 * 5 = 45.
Therefore, the LCM of 15 and 45 is 45 seconds.
Since the two lights flashed together at 3 p.m., the two lights will flash together again after 45 seconds. Adding this duration to 3 p.m. gives us the time of the next simultaneous flash.
So, the next time the two lights will flash together is at 3:00 p.m. + 45 seconds, which is 3:00 p.m. and 45 seconds.