What are the common multiples of 9 and 12?

Common multiples of 9 and 12 are numbers that both 9 and 12 can be divided into evenly with no remainder.

To find the common multiples of 9 and 12, we compare the list of multiples of 9 with the list of multiples of 12 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 12, we multiply 12 by 1, 12 by 2, and so on like this:

12 x 1 = 12
12 x 2 = 24
12 x 3 = 36
12 x 4 = 48
...

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 12?"

36, 72, 108, 144, etc.

Since 36 is the first number they have in common, 36 is the least common multiple of 9 and 12.

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 36 (the least common multiple), so you can continue the green list above with more common multiples of 9 and 12 by simply adding 36 to the last number on the list.

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