Three bells toll regularly at intervals of 8 minutes, 12 minutes and 18 minutes respectively. Find the time gap between two successive instances of all 3 bells tolling together.1 hour 6 minutes1 hour 12 minutes2 hours 24 minutes1 hour 18 minutes
Question
Three bells toll regularly at intervals of 8 minutes, 12 minutes and 18 minutes respectively. Find the time gap between two successive instances of all 3 bells tolling together.1 hour 6 minutes1 hour 12 minutes2 hours 24 minutes1 hour 18 minutes
Solution
To find the time gap between two successive instances of all 3 bells tolling together, we need to find the least common multiple (LCM) of the three given intervals.
The given intervals are 8 minutes, 12 minutes, and 18 minutes.
Step 1: Prime factorize the numbers 8 = 2^3 12 = 2^2 * 3 18 = 2 * 3^2
Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime factors obtained from the numbers. So, LCM = 2^3 * 3^2 = 8 * 9 = 72 minutes
Therefore, the time gap between two successive instances of all 3 bells tolling together is 72 minutes, which is 1 hour 12 minutes. So, the correct answer is 1 hour 12 minutes.
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