Question

Imagine a steady beat, like a drum beating every second. If you were to clap on every other beat and say "year" on every third beat, when would the two sounds happen at the same time?

How does this relate to common factors or common multiples?

Answer 1

Answer: They would be at the same time on the 6th beat

By giving 1/2 and 1/3 a common denominator, you are able to find when they would first overlap.

Explanation:

1/2 and 1/3 have a LCD of 6, thus making them overlap on the 6th beat

Answer 2

The phase isn't specified; let's say we clap on beats 2 4 6 8 10 12 ... and talk on beats 3 6 9 12 15 ...

We see we do both on beats 6 12 18 24 ...

We sync every 6 beats, 6 being the least common multiple of 2 and 3.