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The **lowest common denominator** (**LCD**) for a number of fractions is the lowest number that is a multiple of all the denominators. It is the lowest denominator that all the fractions can be rewritten with by expanding the fractions, i.e. by multiplying the numerator and denominator with the same number.

The lowest common denominator can be useful when simplifying or calculating additions and subtractions of fractions. If multiple terms are fractions with the same denominator they can be combined into one fraction which makes it easier to simplify the numerator terms.

Here is an example that demonstrates how the lowest common denominator can be used to calculate the addition of two fractions.

5

2

+ 2

1

3

3

These two fractions have a lowest common denominator of LCD(2, 3) = 6. This means that both fractions can be expanded so that they get a denominator value of 6. The first fraction is expanded by multiplying both the numerator and denominator by 3. The same thing is done for the second fraction except that a multiplication factor of 2 is used instead.

5 × 3

2 × 3

+ 2 × 3

1 × 2

3 × 2

=
3 × 2

15

6

+ 6

2

6

6

Now that the fractions have the same denominator they can be combined on the same fractional line so that the sum in the numerator can easily be calculated.

15 + 2

6

=
6

17

6

6

Calculate the greatest common divisor for two or more integers.