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Answer :
The bells will toll together 15 times in 2 hours because their least common multiple occurs every 504 seconds, fitting into the 7200-second timeframe 14 times with a remainder, allowing for one additional tolling event.therefore the corect option D
First, we calculate the time in seconds for 2 hours:
[tex]\[ 2 \text{ hours} \times 60 \text{ minutes/hour} \tim[/tex] es 60[tex]\text{ seconds/minute} = 7200 \text{ seconds} \][/tex]
Next, we find the least common multiple (LCM) of the time intervals at which the bells toll:
[tex]\[ LCM(6, 7, 8, 9) = 2^3 \times 3^2 \times 7 = 504 \text{ seconds} \][/tex]
To determine how many times the bells will toll together in 2 hours, we divide the total time by the LCM:
[tex]\[ \frac{7200 \text{ seconds}}{504 \text{ seconds}} \approx 14 \text{ with a remainder of } 288 \text{ seconds} \][/tex]
The remainder of 288 seconds is less than the LCM, which means there will be one more instance of all the bells tolling together before the 2 hours are completed.
Therefore, the total number of times the bells will toll together in 2 hours is 14 + 1 = 15 times, which corresponds to option D.
therefore the corect option D
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