Aus Online Mathematik Brückenkurs 1

We divide up the two numerators into the smallest possible integer factors,

\displaystyle \begin{align} & 12=2\centerdot 6=2\centerdot 2\centerdot 3 \\ & 14=2\centerdot 7 \\ \end{align}

The expression can thus be written as

\displaystyle \frac{1}{2\centerdot 2\centerdot 3}-\frac{1}{2\centerdot 7}

Here, we see that the denominators have a factor \displaystyle 2 in common. We multiply the top and bottom of the first fraction by \displaystyle 7 and the second by \displaystyle 2\centerdot 3 i.e. we leave out the common factor \displaystyle 2, so that the fractions have the lowest common denominator \displaystyle 2\centerdot 2\centerdot 3\centerdot 7,

\displaystyle \frac{1}{12}-\frac{1}{14}=\frac{1}{2\centerdot 2\centerdot 3}-\frac{1}{2\centerdot 7}=\frac{1}{2\centerdot 2\centerdot 3}\centerdot \frac{7}{7}-\frac{1}{2\centerdot 7}\centerdot \frac{2\centerdot 3}{2\centerdot 3}

The lowest common denominator is \displaystyle 84.