What are the common multiples of 31 and 23?

Common multiples of 31 and 23 are numbers that both 31 and 23 can be divided into evenly with no remainder.

To find the common multiples of 31 and 23, we compare the list of multiples of 31 with the list of multiples of 23 to see what they have in common.

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
...

Similarly, to create a list of multiples of 23, we multiply 23 by 1, 23 by 2, and so on like this:

23 x 1 = 23
23 x 2 = 46
23 x 3 = 69
23 x 4 = 92
...

When we compare the two lists to see what they have in common, we get the answer to "What are the common multiples of 31 and 23?"

713, 1426, 2139, 2852, etc.

Since 713 is the first number they have in common, 713 is the least common multiple of 31 and 23.

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 713 (the least common multiple), so you can continue the green list above with more common multiples of 31 and 23 by simply adding 713 to the last number on the list.

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