Question

Five bells begin to toll together and toll respectively at intervals of $6,5,7,10$ and $12$ seconds. How many times will they toll together in one hour excluding the one at the start.

• A. $7$ times
• B. $8$ times
• C. $9$ times
• D. $11$ times

Answer 1

The correct option is B

$8$ times

Step 1. Find the LCM

To toll together we need to take the LCM of each seconds of bell

Factor of $6$ is

$6=2\times 3$

Factor of $5$ is

$5=1\times 5$

Factor of $7$ is

$7=1\times 7$

Factor of $10$ is

$10=2\times 5$

Factor of $12$ is

$12=2\times 2\times 3$

Therefore the LCM of $6,5,7,10$ and $12$ is

LCM$\left(6,7,5,10,12\right)=420$

Step 2. Find the interval of time at which they toll together.

We know that

$420\mathrm{seconds}$$=7\mathrm{minutes}$ $[\because 1\mathrm{minutes}=60\mathrm{seconds}]$

So the bells will toll together after every $7$$\mathrm{minutes}$

We know that

$1\mathrm{hour}=60\mathrm{minutes}$

Therefore the bell will toll together $8$ times $\left[\because 8\times 7=56\right]$ excluding the one at the start.

Hence the correct option is $\mathrm{B}$.