Red, Green and Yellow light of a traffic signal blinks at an interval of 15 second, 20 second and 25 second. If they all blinks together at 9:00 AM then at what time they will again blink simultaneously.9:12 AM9:05 AM9:08 AM9:06 AM
Question
Red, Green and Yellow light of a traffic signal blinks at an interval of 15 second, 20 second and 25 second. If they all blinks together at 9:00 AM then at what time they will again blink simultaneously.9:12 AM9:05 AM9:08 AM9:06 AM
Solution
To solve this problem, we need to find the least common multiple (LCM) of the three given intervals (15 seconds, 20 seconds, and 25 seconds). The LCM of these numbers will give us the time in seconds when all three lights will blink together again.
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First, let's find the prime factors of each number:
- 15 = 3 * 5
- 20 = 2 * 2 * 5
- 25 = 5 * 5
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Now, let's find the LCM. The LCM is found by multiplying the highest power of all the prime numbers in the numbers we are considering.
- The highest power of 2 in our numbers is 2 (from 20),
- The highest power of 3 is 1 (from 15),
- The highest power of 5 is 2 (from 25).
So, LCM = 2^2 * 3^1 * 5^2 = 4 * 3 * 25 = 300 seconds.
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Convert 300 seconds to minutes by dividing by 60 (since there are 60 seconds in a minute). 300 / 60 = 5 minutes.
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If the lights all blinked together at 9:00 AM, they will all blink together again 5 minutes later, at 9:05 AM.
So, the correct answer is 9:05 AM.
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