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  • 26. 4 Bells toll together at 9.00 am. They toll after 7, 8, 11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours?

4 Bells toll together at 9.00 am. They toll after 7, 8, 11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours?

Answers (1)

best_answer

They will toll together again after a time equal to the LCM of their intervals.
Intervals $=7,8,11,12$ seconds
Prime factors:
* 7=7
* $8=2^3$
* 11 = 11
* $12=2^2 \times 3$

LCM $=2^3 \times 3 \times 7 \times 11=8 \times 3 \times 7 \times 11=1848$ seconds
So, they toll together every 1848 seconds = 30 minutes 48 seconds

Total time = $\mathbf{3}$ hours = 180 minutes = 10800 seconds
Number of times they toll together after 9:00 am:

$$
\frac{10800}{1848} \approx 5.84
$$

So they toll together 5 full times within 3 hours.

Posted by

Vishal kumar

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