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# What is the difference between a least common multiple and a least common denominator?

The Least (or Lowest) Common Multiple (LCM) is the smallest number that is a multiple of both numbers.

For example: the LCM of 10 and 4 is 20, because both 10 and 4 go into 20 and 20 is the smallest number both 10 and 4 can go into.

To be able to add or subtract fractions they must have the same denominator. If the denominators are different then the fractions must first be converted into equivalent fractions with a common denominator; any common denominator can be used, but by using the Least Common Multiple of the denominators as the new denominator it keeps the numbers smaller; this smallest denominator is known as the Least Common Denominator

Thus the Least Common Denominator is the Least Common Multiple of the denominators of two (or more) fractions (used when adding or subtracting fractions with different denominators).

As the Least Common Multiple is used most often with adding or subtracting fractions, it is often referred to as the Least Common Denominator (because the numbers being considered are usually denominators of fractions).

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