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?

By K Balaji|Updated : November 12th, 2022

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively. They toll 16 times collectively in 30 hours.

It is given that six bells start tolling simultaneously and ring every 2, 4, 6, 8, or 12 minutes.

We must determine the LCM of 2, 4, 6, 8, 10, and 12 to determine the duration for six bells to ring simultaneously.

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 ?

LCM = 2 × 2 × 3 × 2 × 5 = 120

Hence, after each 120 seconds, they would toll together.

Consequently, the number of times they toll together in 30 minutes = (30 x 60 seconds)/ 120 seconds

= 15 times

However, the query states that they all start tolling at once. They essentially toll at the so the combined tolls result from that is = 15 + 1 = 16

LCM

Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple. The acronym LCM stands for the least common multiple or factor of any two or more specified integers.

Methods of LCM

There are three key approaches we can use to determine the LCM of two or more numbers. As follows:

  1. Listing the Multiples
  2. Prime Factorisation Method
  3. Division Method

Summary:-

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, they toll together 16 times

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