Question

Three bells ring at intervals of 36 seconds, 40 seconds and 48 seconds respectively. If they ring together now, then how many minutes later they ring together again?

• A. $6$ minutes
• B. $12$ minutes
• C. $18$ minutes
• D. $24$ minutes

Answer 1

The correct option is B $12$ minutes

To find the time in which all the bells ring together, we need to find the LCM of $36,40,48.$
Prime factorization of $36=2\times 2\times 3\times 3$
Prime factorization of $40=2\times 2\times 2\times 5$
Prime factorization of $48=2\times 2\times 2\times 2\times 3$
Hence, LCM of $36,40,48=2\times 2\times 2\times 2\times 3\times 3\times 5=720$ seconds.

$720\text{seconds}=\frac{720}{60}\text{minutes}=12\text{minutes}$

Hence, all the bells will ring together after $12$ minutes.