 # Find the Common Denominator Using the Times Tables

There are several methods for finding the lowest common factor. I will show you one where you search through the times tables, and one that works no matter what numbers you have.

## Searching for the Lowest Common Denominator in the Times Tables

When you want to find the lowest common denominator, you can look through the times tables. In the example below, one of the fractions has $8$ as its denominator, and the other has $20$. Then you have to find a number you can multiply with $8$ to make a multiple of $20$.

There are no integers that give you $20$ when multiplied by $8$. As $20$ is the largest of the two denominators, you should look at the next multiple of $20$, which is $20\cdot 2=40$. Then you can check if there’s an integer that gives you $40$ when multiplied by $8$. There is! $8\cdot 5=40$. That means you can expand the first fraction by $5$ and the other by $2$.

Example 1

Find $\frac{3}{8}-\frac{7}{20}$.

$\begin{array}{llll}\hfill \frac{3}{8}-\frac{7}{20}& =\frac{3\cdot 5}{8\cdot 5}-\frac{7\cdot 2}{20\cdot 2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{15}{40}-\frac{14}{40}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{15-14}{40}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{1}{40}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$