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# Least common denominator of fractions.

Any two fractions it is possible to reduce to the same denominator, or otherwise to the common denominator.

Definition.
The least common denominator is the least common multiple of the denominators of a set of vulgar fractions. It is the smallest positive integer that is a multiple of the denominators.

## For reduction of fractions to the least common denominator you should:

• find the least common multiple of the denominators [it will be the least common denominator];
• divide the least common denominator into denominators of the given fractions [it means to find for each fraction an additional multiplier];
• to multiply numerator and denominators of each fraction by its additional multiplier.

## Examples of tasks: reduce fractions to least common denominator

Example 1.
To reduce to a common denominator fractions: 56 and 49.

lcd(6, 9) = 18

18/6 = 3 — additional multiplier of the first fraction,
18/9 = 2 — additional multiplier of the second fraction.

Then:

 5 = 5·3 = 15 6 6·3 18

 4 = 4·2 = 8 9 9·2 18

Example 2.
To reduce to a common denominator fractions: 227 and 336.

lcd(27, 36) = 108

108/27 = 4 — additional multiplier of the first fraction,
108/36 = 3 — additional multiplier of the second fraction.

Then:

 2 = 2·4 = 8 27 27·4 108

 3 = 3·3 = 9 36 36·3 108