How to Find the Least Common Multiple of Two Numbers
Simply put, the least common multiple (LCM) is the smallest number into which two (or more) numbers can divide. Although you can use a calculator to help with the answer, understanding the basic rules of multiplication can help you determine the answer. There are a couple ways to find the least common multiple, so use whichever way you feel comfortable.
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Instructions
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First Method
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1
List the multiples of both numbers. For example, you're trying to find the least common multiple of 9 and 12.
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2
Multiply both 9 and 12 by 2, 3, 4, etc. The multiples of 9 are: 18, 27, 36, 45, 54, 63, 72 and 81. The multiples of 12 are: 24, 36, 48, 60, 72, 84, 96 and 108.
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3
Examine the list, and decide which is the smallest number that both lists have in common. In Step 2, 36 is the number that both lists have in common. Therefore, 36 is the least common multiple.
Second Method
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Determine the greatest common factor between the two numbers. Again, use the numbers 9 and 12. The greatest common factor is 3.
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5
Multiply the numbers 9 and 12. The number you get is 108.
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6
Divide the answer you get in Step 2 by the greatest common factor from Step 1. In this example, divide 108 by 3. The answer is 36, which is the least common multiple.
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Tips & Warnings
If you don't want to make a long list of multipliers, this method might work best for you.
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Comments
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I want to get some close friends.
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this was very helpful... I was totally lost before I read this thank you very much! but I got a question... what if there is no gcf?
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thank you.....
