What are the common multiples of 9 and 21?

Common multiples of 9 and 21 are numbers that both 9 and 21 can be divided into evenly with no remainder.

To find the common multiples of 9 and 21, we compare the list of multiples of 9 with the list of multiples of 21 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 21, we multiply 21 by 1, 21 by 2, and so on like this:

21 x 1 = 21
21 x 2 = 42
21 x 3 = 63
21 x 4 = 84
...

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 21?"

63, 126, 189, 252, etc.

Since 63 is the first number they have in common, 63 is the least common multiple of 9 and 21.

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 63 (the least common multiple), so you can continue the green list above with more common multiples of 9 and 21 by simply adding 63 to the last number on the list.

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What are the common multiples of 9 and 22?
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