The simplest way to find a typical denominator is come "skip count" (count by multiples) by each of the numbers in question. Because that example, 9, 18, 27, 36, 45, 54, 63, 72 . . . And also 12, 24, 36, 48, 60, 72, 84, . . . . Any kind of numbers on both lists room "common denominators" (36 and also 72); the an initial such number on both perform is the Lowest typical Denominator (LCD).

You are watching: Common denominator of 9 and 12

A more complex way entails using the element factorizations that the numbers in question. The p. F. Because that 9 = 3 x 3; the p. F. Because that 12 = 2 x 2 x 3. Next, heat the two p.f."s up favor this, showing where any type of factors indigenous the p.f."s overlap:

2 x 2 x 3

3 x 3

Now, create the determinants out in one line, making use of all the determinants from the 2 lines, however where lock overlap, write only among the 2 overlapping factors:

2 x 2 x 3 x 3 = 36 (the LCD)


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A denominator is the number top top the bottom in a fraction. In this case, 9 and also 12 are both totality numbers. The common denominator would be 1 due to the fact that both numbers would have actually a fraction of 9/1 and also 12/1. However, if 9 and 12 space denominators to fractions (i.e. 1/9 and also 1/12) that would be a different story. In this situation you would uncover the smallest number the both numbers deserve to be separated in come completely.

For example:

9 and 12 have the right to both be divided into 36

36 / 9 = 4

36 / 12 = 3

Now you deserve to just multiply each fraction by the respective number to get fractions over 36.

1 / 9 multiply both the top and also the bottom number by 4 offering you 4 / 36

1 / 12 multiply both the top and the bottom number by 3 offering you 3 / 36

Your common denominator would be 36.

Another means to uncover this would be to multiply each fraction by the various other fractions denominator.

I.E. 9 * 12 = 108

(1 / 9) * (12 / 12) = 12 / 108

(1 / 12) * (9 / 9) = 9 / 108


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