What are the common multiples of 6 9 15 and 18?

Answer 1

The multiples of 6, 9, 15, and 18 are the infinite set of the multiples of their LCM, which is 90. So the common multiples of 6, 9, 15, and 18 are 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, and so on.

Explanation -- The LCM

First, let's prime factorize each of the numbers:

6: 2 x 3

9: 3 x 3

15: 3 x 5

18: 2 x 3 x 3

We now need to calculate the least common multiple (LCM) of these numbers by making sure that each number's factors are represented (for example, 6 requires that there be at least one 2 and one 3; the 9 requires that there be at least two 3s).

So we have 2 x 3 x 3 x 5.

Note that included in the above are 2 x 3, 3 x 3, 3 x 5, and 2 x 3 x 5, each of the factors of the numbers.

This gives us 2 x 3 x 3 x 5 = 90. Calculating other Multiples

1. Thus the LCM (least common factor) is 90. To find other multiples we can calculate 90 * x where x can be any whole number.

For example we can have

2 x 90 = 180, so 180 is a multiple of 6, 9, 15, and 18.

1.5 x 90 = 135, so 135 is a multiple.

Extension

We can even extend this to a more algebraic problem:

If c represents any whole number, then c x 90 = 90c would also be a whole number which would constitute it as a multiple