Common multiples of 2 8 12?

Answer 1

To find a common multiple of 2, 8, and 12, we need to look at their prime factorization (the stuff you multiply together to get those numbers).

2 is prime.

8 = 2*2*2.

12 = 2*2*3.

So, if we want to have a number that is a common multiple of 2, 8, and 12, it must be composed of the greatest amount of each prime number that 2, 8, and 12 have.

So, it must be at least 2*2*2 * 3 = 24.

So any common multiple will be of the form 24 * k, where k is any integer. So for example:

k=1, 2, 3, 4, ...

24, 48, 72, 96, etc...