Answer :
♀️ Offer your prayers to Lord Ganesha with reverence and devotion, seeking his divine grace to overcome challenges and attain success in all endeavors.
via -bobble.in/ganesha
Answer:
To determine when the three bells will ring together again, we need to find the least common multiple (LCM) of their ringing intervals: 15 minutes, 24 minutes, and 36 minutes.
**Step 1: Prime Factorization**
First, we find the prime factors of each interval:
- \( 15 = 3 \times 5 \)
- \( 24 = 2^3 \times 3 \)
- \( 36 = 2^2 \times 3^2 \)
**Step 2: Identify the Highest Powers of Each Prime**
Next, we identify the highest powers of each prime number that appear in these factorizations:
- The highest power of \( 2 \) is \( 2^3 \) (from 24).
- The highest power of \( 3 \) is \( 3^2 \) (from 36).
- The highest power of \( 5 \) is \( 5 \) (from 15).
**Step 3: Calculate the LCM**
The LCM is found by multiplying these highest powers together:
{LCM} = 2^3 \times 3^2 \times 5
Calculating this:
2^3 = 8
3^2 = 9
8 \times 9 = 72
72 \times 5 = 360
So, the LCM of 15, 24, and 36 is 360 minutes.
**Step 4: Determine the Time**
Since the bells ring together at 2:00 PM, we add 360 minutes to this time to find when they will ring together again.
360 \text{ minutes} = 6 \text{ hours}
Adding 6 hours to 2:00 PM:
2:00 \, \text{PM} + 6 \, \text{hours} = 8:00 \, \text{PM}
Therefore, the three bells will ring together again at 8:00 PM.