What are the common multiples of 13 and 30?

Common multiples of 13 and 30 are numbers that both 13 and 30 can be divided into evenly with no remainder.

To find the common multiples of 13 and 30, we compare the list of multiples of 13 with the list of multiples of 30 to see what they have in common.

To create a list of multiples of 13, we multiply 13 by 1, 13 by 2, and so on like this:

13 x 1 = 13
13 x 2 = 26
13 x 3 = 39
13 x 4 = 52
...

Similarly, to create a list of multiples of 30, we multiply 30 by 1, 30 by 2, and so on like this:

30 x 1 = 30
30 x 2 = 60
30 x 3 = 90
30 x 4 = 120
...

When we compare the two lists to see what they have in common, we get the answer to "What are the common multiples of 13 and 30?"

390, 780, 1170, 1560, etc.

Since 390 is the first number they have in common, 390 is the least common multiple of 13 and 30.

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 390 (the least common multiple), so you can continue the green list above with more common multiples of 13 and 30 by simply adding 390 to the last number on the list.

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What are the common multiples of 13 and 31?
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