Three bell rang together at 4:30 pm. Bell A rings after every 12minutes and Bell B after every 15minutes and Bell C after every 18minutes. At what time will these bells ring together again
To determine when the three bells will ring together again, we need to find the least common multiple (LCM) of 12, 15, and 18.
First, we find the prime factorization of each number:
12 = 2^2 * 3
15 = 3 * 5
18 = 2 * 3^2
Next, we take the highest power of each prime factor that appears in any of the numbers:
- The highest power of 2 is 2^2.
- The highest power of 3 is 3^2.
- The highest power of 5 is 5.
Multiplying these together, we get the LCM:
LCM = 2^2 * 3^2 * 5 = 4 * 9 * 5 = 180.
Therefore, the three bells will ring together again in 180 minutes.
To convert this to hours and minutes, we divide 180 by 60:
180 ÷ 60 = 3 hours.
So, the three bells will ring together again 3 hours after 4:30 pm, which is at 7:30 pm.