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What is the least possible number of planks of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length?
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Step-by-step solution
3 stepsFind the least common multiple (LCM) of the tolling intervals.
The bells toll after 7, 8, 11, and 12 seconds.
First, find the prime factorization of each number:
The LCM is the product of the highest powers of all prime factors present:
This means the bells will toll together every 1848 seconds.
Convert the given time duration into seconds.
The question asks about the next 3 hours.
1 hour = 60 minutes
1 minute = 60 seconds
1 hour = seconds
3 hours = secondsCalculate how many times the bells will toll together again in the next 3 hours.
The bells toll together at 9:00 a.m. We need to find how many times they toll together after this initial time within the 3-hour period.
Divide the total time in seconds by the LCM:Since we are looking for the number of complete tolling cycles within the 3 hours, we take the floor of this value.
The bells will toll together 5 more times within the next 3 hours.The final answer is .
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