Question

Three bells chime at an interval of 18 min, 24 min and 32 min. At a certain time they begin to chime together. What length of time will elapse before they chime together again?

• A. 2 hr and 24 min
• B. 4 hr and 48 min
• C. 1 hr and 36 min
• D. 5 hr

Hint:

For problems involving events repeating at different intervals, always calculate the LCM of the times to find when they coincide again.

Answer 1

The Correct Option is A

We need to find the Least Common Multiple (LCM) of 18, 24, and 32 minutes. First, prime factorization: \[ 18 = 2 \times 3^2, \quad 24 = 2^3 \times 3, \quad 32 = 2^5 \] LCM is obtained by taking the highest powers of all primes present: \[ \text{LCM} = 2^5 \times 3^2 = 32 \times 9 = 288 \ \text{minutes} \] Convert 288 minutes to hours: \[ 288 \ \text{minutes} = 4 \ \text{hours} \ 48 \ \text{minutes} \] Thus, the bells will chime together again after 4 hr 48 min.