What are the common multiples of 42 and 75?

Common multiples of 42 and 75 are numbers that both 42 and 75 can be divided into evenly with no remainder.

To find the common multiples of 42 and 75, we compare the list of multiples of 42 with the list of multiples of 75 to see what they have in common.

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
...

Similarly, to create a list of multiples of 75, we multiply 75 by 1, 75 by 2, and so on like this:

75 x 1 = 75
75 x 2 = 150
75 x 3 = 225
75 x 4 = 300
...

When we compare the two lists to see what they have in common, we get the answer to "What are the common multiples of 42 and 75?"

1050, 2100, 3150, 4200, etc.

Since 1050 is the first number they have in common, 1050 is the least common multiple of 42 and 75.

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 1050 (the least common multiple), so you can continue the green list above with more common multiples of 42 and 75 by simply adding 1050 to the last number on the list.

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What are the common multiples of 42 and 76?
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