What are the common multiples of 33 and 67?

Common multiples of 33 and 67 are numbers that both 33 and 67 can be divided into evenly with no remainder.

To find the common multiples of 33 and 67, we compare the list of multiples of 33 with the list of multiples of 67 to see what they have in common.

To create a list of multiples of 33, we multiply 33 by 1, 33 by 2, and so on like this:

33 x 1 = 33
33 x 2 = 66
33 x 3 = 99
33 x 4 = 132
...

Similarly, to create a list of multiples of 67, we multiply 67 by 1, 67 by 2, and so on like this:

67 x 1 = 67
67 x 2 = 134
67 x 3 = 201
67 x 4 = 268
...

When we compare the two lists to see what they have in common, we get the answer to "What are the common multiples of 33 and 67?"

2211, 4422, 6633, 8844, etc.

Since 2211 is the first number they have in common, 2211 is the least common multiple of 33 and 67.

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 2211 (the least common multiple), so you can continue the green list above with more common multiples of 33 and 67 by simply adding 2211 to the last number on the list.

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What are the common multiples of 33 and 68?
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