Three bells toll at intervals of 36 sec, 40 sec, and 48 sec respectively. They…

To find when the three bells will toll together again, you need to find the Least Common Multiple (LCM) of their tolling intervals. Since the bells start together, they will next toll together at a time interval that is a multiple of all three individual intervals.

Step-by-Step Calculation

1. Identify the intervals:

• Bell 1: 36 seconds

• Bell 2: 40 seconds

• Bell 3: 48 seconds

2. Find the prime factorization for each interval:

• 36 = 2² × 3²

• 40 = 2³ × 5¹

• 48 = 2⁴ × 3¹

3. Determine the LCM: The LCM is found by taking the highest power of each prime factor present in any of the numbers:

• Prime factor 2: The highest power is 2⁴ (from 48).

• Prime factor 3: The highest power is 3² (from 36).

• Prime factor 5: The highest power is 5¹ (from 40).

• LCM = 2⁴ × 3² × 5¹ = 16 × 9 × 5 = 720 seconds.

4. Convert the time to minutes: Since there are 60 seconds in a minute:

• 720 seconds / 60 seconds/minute = 12 minutes.