What are the common multiples of 97 and 53?

Common multiples of 97 and 53 are numbers that both 97 and 53 can be divided into evenly with no remainder.

To find the common multiples of 97 and 53, we compare the list of multiples of 97 with the list of multiples of 53 to see what they have in common.

To create a list of multiples of 97, we multiply 97 by 1, 97 by 2, and so on like this:

97 x 1 = 97
97 x 2 = 194
97 x 3 = 291
97 x 4 = 388
...

Similarly, to create a list of multiples of 53, we multiply 53 by 1, 53 by 2, and so on like this:

53 x 1 = 53
53 x 2 = 106
53 x 3 = 159
53 x 4 = 212
...

When we compare the two lists to see what they have in common, we get the answer to "What are the common multiples of 97 and 53?"

5141, 10282, 15423, 20564, etc.

Since 5141 is the first number they have in common, 5141 is the least common multiple of 97 and 53.

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 5141 (the least common multiple), so you can continue the green list above with more common multiples of 97 and 53 by simply adding 5141 to the last number on the list.

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What are the common multiples of 97 and 54?
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