What are the common multiples of 9 and 17?

Common multiples of 9 and 17 are numbers that both 9 and 17 can be divided into evenly with no remainder.

To find the common multiples of 9 and 17, we compare the list of multiples of 9 with the list of multiples of 17 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 17, we multiply 17 by 1, 17 by 2, and so on like this:

17 x 1 = 17
17 x 2 = 34
17 x 3 = 51
17 x 4 = 68
...

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 17?"

153, 306, 459, 612, etc.

Since 153 is the first number they have in common, 153 is the least common multiple of 9 and 17.

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 153 (the least common multiple), so you can continue the green list above with more common multiples of 9 and 17 by simply adding 153 to the last number on the list.

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