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How to Find the Least Common Denominator of a Pair of Fractions With Different Denominators

A fraction consists of a set of numbers denoting the relationship of a part to a whole. The top number is referred to as the numerator, and the bottom number as the denominator. If you are going to add or subtract fractions, you must have the same number in the denominator of both fractions. This is known as a common denominator. The least common denominator is the lowest number that both denominators will fit into evenly.

Instructions

    • 1

      Multiply the two denominators together. For example, if you have 4/9 and 6/15, multiply 9 and 15 to get 135.

    • 2

      Determine the greatest common factor of the two denominators. The greatest common factor is the largest number that will divide into both denominators evenly. In the example of denominators 9 and 15, the greatest common factor is 3.

    • 3

      Divide your answer from Step 1 by the greatest common factor from Step 2. In this example, you would divide 135 by 3 to get 45. This is the least common denominator.

    • 4

      Rewrite the fractions with the least common denominator and the appropriate numerators. The numerators must be multiplied by the quotient of the least common denominator divided by the original denominator. For example, the original fractions were 4/9 and 6/15. The two new fractions will have 45 in the denominators. If you divide 45 by 9, you get 5. Then you multiply 5 times the numerator (4) to get the new fraction, 20/45. For the second fraction, you divide 45 by 15 to get 3 and multiply the numerator (6) times 3 to get the revised fraction, 18/45.

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