Least common denominator of fractions.

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.

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

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