What are the common multiples of 36 and 42?

Common multiples of 36 and 42 are numbers that both 36 and 42 can be divided into evenly with no remainder.

To find the common multiples of 36 and 42, we compare the list of multiples of 36 with the list of multiples of 42 to see what they have in common.

To create a list of multiples of 36, we multiply 36 by 1, 36 by 2, and so on like this:

36 x 1 = 36
36 x 2 = 72
36 x 3 = 108
36 x 4 = 144
...

Similarly, to create a list of multiples of 42, we multiply 42 by 1, 42 by 2, and so on like this:

42 x 1 = 42
42 x 2 = 84
42 x 3 = 126
42 x 4 = 168
...

When we compare the two lists to see what they have in common, we get the answer to "What are the common multiples of 36 and 42?"

252, 504, 756, 1008, etc.

Since 252 is the first number they have in common, 252 is the least common multiple of 36 and 42.

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 252 (the least common multiple), so you can continue the green list above with more common multiples of 36 and 42 by simply adding 252 to the last number on the list.

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