What are the common multiples of 17 and 45?

Common multiples of 17 and 45 are numbers that both 17 and 45 can be divided into evenly with no remainder.

To find the common multiples of 17 and 45, we compare the list of multiples of 17 with the list of multiples of 45 to see what they have in common.

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
...

Similarly, to create a list of multiples of 45, we multiply 45 by 1, 45 by 2, and so on like this:

45 x 1 = 45
45 x 2 = 90
45 x 3 = 135
45 x 4 = 180
...

When we compare the two lists to see what they have in common, we get the answer to "What are the common multiples of 17 and 45?"

765, 1530, 2295, 3060, etc.

Since 765 is the first number they have in common, 765 is the least common multiple of 17 and 45.

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 765 (the least common multiple), so you can continue the green list above with more common multiples of 17 and 45 by simply adding 765 to the last number on the list.

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What are the common multiples of 17 and 46?
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