Question

One bell strikes at every 6 seconds the secon bell strikes at every 9 seconds and third bell strikes at every 12 seconds when eill they all strike?

Answer 1

These all bells will strike again at their common multiple.
The latest common multiple would be the lcm of them.
LCM of 6,9,12 = 2^2 × 3^2 = 4 × 9 = 36
They will strike together at 36th second

Answer 2

The bells will strike together at 36th second

Solution:

Given that,

One bell strikes at every 6 seconds

Second bell strikes at every 9 seconds

Third bell strikes at every 12 seconds

We have to find out when they will strike again

This means, we have to find least common multiple of 6, 9, 12

Find LCM of 6, 9, 12

List all prime factors for each number.

Prime Factorization of 6 is:  2 x 3

Prime Factorization of 9 is:  3 x 3

Prime Factorization of 12 is:  2 x 2 x 3  

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 3, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 3 = 36

Thus they will strike together at 36th second

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