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How to Find the Lowest Common Denominator

The lowest common denominator (LCD) of two fractions is the smallest positive integer that is a multiple of both denominators. The LCD is used when adding or subtracting fractions with different denominators; by expressing both fractions with the same denominator, adding or subtracting them is simply a matter of adding or subtracting their numerators.

Things You'll Need

  • Paper and pencil
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Instructions

    • 1

      Identify the denominators. The denominator is the number on the bottom of a fraction; the number on the top of the fraction is called the numerator. For example. the denominator of 1/3 is 3; the denominator or 5/16 is 16.

    • 2

      Write out the factors of each denominator. The factors of a denominator are like the factors for any other integer: all of the numbers that divide evenly into it. For example, the factors of 16 are 1, 2, 4, 8 and 16; the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

    • 3

      Identify the greatest common factor (GCF) of the two denominators. The GCF is just what it sounds like: the largest number that's a factor of both. For example, the GCF of 16 and 24 is 8, as it is the largest number that's a factor of both 16 and 24.

    • 4

      Multiply the denominators of the two fractions, then divide the product by their greatest common factor. For example, to find the lowest common denominator of 1/16 and 1/24, multiply the denominators:

      16 * 24 = 384

      The GCF of 16 and 24 is 8, so divide the result by 8:

      384 / 8 = 48

      The LCD of 1/16 and 1/24 is 48.

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