Answer :
Answer:
They will flash together at 36 seconds after 8:00 p.M which can be written as 8:00:36 PM.
Step-by-step explanation:
This question can be solved using concept of LCM
LCM is the least number which is divisible by all the set of given number.
LCM is found by finding the prime factors of given set of numbers and then taking the each numbers highest power and then multiplying all.
for example
lets find LCM of 20 and 75
prime factor of 20 = 2*2*5
prime factor of 75 = 3*5*5
highest power of 2 is 2*2 = 4
highest power of 3 is 3 = 3
highest power of 5 is 5*5 = 25
thus LCM is 4*3*25 = 300
Thus, 300 is the least number which will be commonly divisible by 20 and 75.
Now in the problem given One light flashes every 18 seconds and another light flashes every 12 seconds.
Thus, they will will flast together at time when the time will be commonly divisible by both 12 and 18.
to find that time, lets find the LCM of 12 and 18
The number is 12 , 18
prime factor of 12 = 2*2*3
prime factor of 18 = 2*3*3
highest power of 2 is 2*2 = 4
highest power of 3 is 3*3 = 9
thus LCM is 9*4 = 36
Thus, the lights will flash together after 36 seconds.
Given that they flash together at 8:00 p.M
They will flash together at 36 seconds after 8:00 p.M which can be written as 8:00:36 PM.
To determine when two lights will next flash together, one must find the least common multiple of their flash intervals. The next time two lights, one flashing every 18 seconds and the other every 12 seconds, will flash together is 36 seconds past 8:00 p.m., or at 8:00:36 p.m.
The question asks for the next time two lights that flash at different intervals will flash together after a given time. To solve this problem, we need to find the least common multiple (LCM) of the two flash intervals. One light flashes every 18 seconds and another flashes every 12 seconds. To find the LCM of 18 and 12, we list the multiples of these numbers until we find the smallest multiple they have in common.
- Multiples of 18: 18, 36, 54, 72, 90...
- Multiples of 12: 12, 24, 36, 48, 60...
The smallest common multiple is 36 seconds. This is the interval at which both lights will flash together. Since they flash together at 8:00 p.m., the next time they will flash together will be 36 seconds after 8:00 p.m. Therefore, the lights will next flash together at 8:00:36 p.m..
