What are the common multiples of 9 and 31?

Common multiples of 9 and 31 are numbers that both 9 and 31 can be divided into evenly with no remainder.

To find the common multiples of 9 and 31, we compare the list of multiples of 9 with the list of multiples of 31 to see what they have in common.

To create a list of multiples of 9, we multiply 9 by 1, 9 by 2, and so on like this:

9 x 1 = 9
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
...

Similarly, to create a list of multiples of 31, we multiply 31 by 1, 31 by 2, and so on like this:

31 x 1 = 31
31 x 2 = 62
31 x 3 = 93
31 x 4 = 124
...

When we compare the two lists to see what they have in common, we get the answer to "What are the common multiples of 9 and 31?"

279, 558, 837, 1116, etc.

Since 279 is the first number they have in common, 279 is the least common multiple of 9 and 31.

Note: Our lists are shortened because they go on forever, but can you see the pattern when you look at the answer in green above? The common multiples are in intervals of 279 (the least common multiple), so you can continue the green list above with more common multiples of 9 and 31 by simply adding 279 to the last number on the list.

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