Two bell toll at intervals of 24 minutes and 36 minutes respectively. if the toll together at 9am, after how many minutes do they toll together again , at the earliest?
Answers
36 = 24 * 1 + 12
24 = 12 * 2 + 0
Therefore , the HCF is 12 and hence they toll at 12 minutes together...
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Given : two bells toll at intervals of 24 minutes and 36 minutes respectively.
To find : the time at which they toll together again, we need to find the LCM (Least Common Multiple) of 24 and 36.
solution :
The prime factors of 24 are 2, 2, 2, and 3.
The prime factors of 36 are 2, 2, 3, and 3.
The LCM of 24 and 36 can be found by taking the highest power of each prime factor.
So, LCM = 2^3 * 3^2 = 72.
This means that the two bells will toll together every 72 minutes.
The bells toll together at 9 am, and the next time they will toll together is after 72 minutes, i.e., at 10:12 am.
Therefore, the two bells will toll together again, at the earliest, after 72 minutes, which is at 10:12 am.
In summary:
Find the LCM of the time intervals of the two bells.
Add the LCM to the time at which the bells last tolled together to find the next time they will toll together.
To learn more about LCM from the given link.
https://brainly.in/question/54179983