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Home » Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively. In 30 hours, how many times do they toll together?
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively. In 30 hours, how many times do they toll together?
CBSE | Class 10 | Exercise 1B | Maths | Real Numbers | RS Aggarwal
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively. In 30 hours, how many times do they toll together?

Answer:

Six bells toll together at intervals of 2,4, 6, 8, 10 and 12 minutes.

Using prime factorization,

2 = 2

4 = 2 × 2

6 = 2 × 3

8 = 2 × 2 × 2

10 = 2 × 5

12 = 2 × 2 × 3

LCM (2, 4, 6, 8, 10, 12) = 23 × 3 × 5

LCM = 120 minutes

Converting minutes to hours,

∴ LCM = 2 hours

The six bells after every 2 hours will toll together.

∴ Required number of times \begin{array}{l} = \left( {\frac{{30}}{2} + 1} \right)\\ = 16 \end{array}

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