Five bells commence tolling together and toll at intervals of 3,6,9,12 and 15 seconds respectively. In 30 minutes, how many times do they toll together?
Answers
Given:
Five bells commence tolling together and toll at intervals of 3,6,9,12 and 15 seconds respectively.
To Find:
In 30 minutes, how many times do they toll together
Solution:
All bells will toll together at the zeroth second.
Next time they will toll together =
LCM(3,6,9,12,15 ) = 180 seconds = 3 minutes
Hence all bells will toll together after every 3minutes
In 30 minutes all bells will toll together
= ( 30/3 +1) = 11 times
Note: That 1 is for tolling together at zeroth second
Hence, All bells will toll together 11 times in 30minutes .
Answer:
Five bells commence tolling together and tolls at intervals 3 , 6 , 9, 12 , 15 sec respectively.
toll altogether at LCM of {3, 6, 9, 12, 15}
prime factor of 3 = 1 × 3
prime factor of 6 = 1 × 2 × 3
prime factor of 9 = 1 × 3 × 3
prime factor of 12 = 1 × 2 × 2 × 3
prime factor of 15 = 1 × 3 × 5
toll altogether = 1 × 2 × 2 × 3 × 3 × 5
= 4 × 9 × 5 = 4 × 45 = 180 sec = 3min
number of times do they toll altogether
= 45 min/3min
= 15
hence, number of time do they toll altogether is 15
Step-by-step explanation:
I Hope it helps you .
Please like my answer and also follow me ...........please friends .