What are the common multiples of 9 and 61?

Common multiples of 9 and 61 are numbers that both 9 and 61 can be divided into evenly with no remainder.

To find the common multiples of 9 and 61, we compare the list of multiples of 9 with the list of multiples of 61 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 61, we multiply 61 by 1, 61 by 2, and so on like this:

61 x 1 = 61
61 x 2 = 122
61 x 3 = 183
61 x 4 = 244
...

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 61?"

549, 1098, 1647, 2196, etc.

Since 549 is the first number they have in common, 549 is the least common multiple of 9 and 61.

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 549 (the least common multiple), so you can continue the green list above with more common multiples of 9 and 61 by simply adding 549 to the last number on the list.

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