Five bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 seconds respectively. In 30 minutes, how many times do they toll together?

Five bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 seconds respectively. In 30 minutes, how many times do they toll together? Correct Answer 16

Given: 

Six bells start tolling together and toll at intervals of 2, 4, 6, 8 10 seconds respectively. 

Concept:

LCM = Least Common Multiple

Calculation:

LCM can be found out by prime factorization

2 = 1 × 2 

4 = 22

6 = 2 × 3

8 = 23

10 = 2 × 5

LCM (2, 4, 6, 8, 10) = 23 × 3 × 5 = 120 

Bells toll together after every 120 seconds. 

Number of tolling the bells in 30 minutes = (30 minutes × 60 seconds)/120

⇒ 1800 seconds/ 120 = 15 

∴ Total number of times of the tolling of bells after they toll for the first time 

⇒ 15 + 1 = 16

Mistake Points
If two bells after 2 seconds and 5 seconds respectively and they start tolling at the same time.

Then, the first bell tolls after every 2, 4, 6 secs.....

⇒ The second bell tolls after every 5, 10, 15 secs

So, they toll together again after 10 seconds, which is the LCM. 

∴ They toll after 10 seconds, that is whenever the time is a common multiple of 2 and 5 both. 

Since the bells start tolling together, the first toll also needs to be counted, that is the number of times of tolling since the first time.