Question

three Bells toll at intervals of 9 12 15 minutes.if they start tolling together,after what time will they next toll together

Answer 1

the next time they'll next toll together is 180 minutes.

Step-by-step explanation:

Time interval for tolling = 9 min, 12 min, and 15 min.

The next time they will toll together will be the LCM of their time intervals.

we find the LCM of the three numbers as shown below

LCM of 9 = 3 x 3 =
`3^(2)`

LCM of 12 = 2 x 2 x 3 =
`2^(2)` x 3

LCM of 15 = 3 x 5

we represent each factor with the factor with the highest power i.e
`3^(2)`,
`2^(2)` and 5

the LCM is then =
`3^(2)`x
`2^(2)` x 5 = 180

the next time they'll next toll together is 180 minutes.