Aus Online Mathematik Brückenkurs 1

A common way to calculate the expression in the exercise is to multiply top and bottom of each fraction by the other fraction's denominator, so as to obtain a common denominator,

\displaystyle \frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{10}{10}+\frac{1}{10}\cdot \frac{6}{6}=\frac{10}{60}+\frac{6}{60}\,.

However, this gives a common denominator, 60, which is larger than it really needs to be.

If we instead divide up the fractions' denominators into their smallest possible integral factors,

\displaystyle \frac{1}{2\cdot 3}+\frac{1}{2\cdot 5}\,,

we see that both denominators contain the factor 2 and it is then unnecessary to include that factor when we multiply the top and bottom of each fraction.

\displaystyle \frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{5}{5}+\frac{1}{10}\cdot \frac{3}{3}=\frac{5}{30}+\frac{3}{30}\,.

This gives the lowest common denominator (LCD), 30.