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
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
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The first five multiples of 6 are 6, 12, 18, 24 and 30. For them to be common, they need to be compared to another set of multiples.
3, 6, 9 and so on. 5, 10, 15 and so on. 6, 12, 18 and so on. Common multiples include 30, 60, 90 and so on.
The common multiples of 2 and 6 are numbers that can be divided evenly by both 2 and 6. To find these common multiples, we first list the multiples of each number. The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc., and the multiples of 6 are 6, 12, 18, 24, 30, 36, etc. The common multiples of 2 and 6 are the numbers that appear in both lists, such as 6, 12, 18, etc.
The common multiples of 6 and 9 are the infinite set of multiples of their LCM, which is 18. So the common multiples of 6 and 9 are 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, and so on.
Do you mean the lowest common multiple? (lcm)?Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27...Common multiples of 2 and 3 include 6, 12, 18, and 24.