Seven guns all commence firing together at a target but they continue to fire at interval 2,3,5,7 and 12 minutes. After how many hours do all five guns fire at the same time as they did in the beginning?
Thanks for helping
The least common multiple is 420.
420 / 60 = 7 hours
The LCM of 2, 3, 5, 7, and 12 is 420
So they will all fire together again 420 minutes, or 7 hours from now
To find the time at which all seven guns fire at the same time as they did in the beginning, we need to find the least common multiple (LCM) of the given intervals - 2, 3, 5, 7, and 12 minutes.
To find the LCM, we can use the prime factorization method. Let's break down the intervals into their prime factors:
2 minutes = 2
3 minutes = 3
5 minutes = 5
7 minutes = 7
12 minutes = 2^2 x 3
Now, we need to take the highest power of each prime factor. In this case, we have:
2^2 x 3 x 5 x 7 = 4 x 3 x 5 x 7 = 420
Therefore, the LCM of the intervals 2, 3, 5, 7, and 12 minutes is 420 minutes.
To convert this to hours, we divide by 60:
420 minutes / 60 = 7 hours
So all seven guns will fire together again after 7 hours.