# Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

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UGC NET Paper 1: Held on 5th Dec 2021 Shift 2
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1. 4
2. 10
3. 16
4. 20

Option 3 : 16

## Detailed Solution

Given:

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively.

Concept used:

Least common multiplication

Calculation:

A least common multiple of (2, 4, 6, 8, 10 and 12)

we can write 2 = 1 × 2

4 = 22

6 = 2 × 3

8 = 23

10 = 2 × 5

12 = 22 × 3

A least common multiple of (2, 4, 6, 8, 10 and 12) = 23 × 3 × 5

⇒ 8 × 3 × 5

⇒ 120 sec

Bells ring together after every 120 sec

Required number of times in 30 minutes (30 × 60 seconds ) = [(30 × 60)/120]

⇒ 15

But we have to add 1 because at starting all bells will be rung once a time after that they ring 15 times.

⇒ 15 + 1

⇒ 16 times

∴ The required number of times when they toll together is 16.
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