Respuesta :
If Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10, and 12 seconds respectively and toll together at 11:00, then they will toll together again at 11:02.
Least common multiple abbreviated as LCM is used to determine the time at which the six bells will toll together again.
The least common multiple of two or more numbers is the smallest number that is a multiple of those numbers.
The least common multiple of 2, 4, 6, 8, 10, and 12 can be found by prime factorization.
Prime factorization of :
2 = 2^1
4 = 2 x 2 = 2^2
6 = 2 x 3
8 = 2^3
10 = 2 x 5
12 = 2 x 2 x 3 = 2^2 x 3
The least common multiple can be calculated by the multiplication of the prime factors raised to their highest power.
Therefore,
LCM = (2^3) (3) (5) = 120
Hence the bells will toll together again after 120 seconds
As 120 seconds = 2 minutes
Therefore, the time at which they will toll together again is calculated to be 11:02.
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