If we want to add or subtract fractions, they need to have the same denominator. If they don't, we'll need to change one or both of our fractions to its equivalent fraction. One way to do this is to find out how their denominators are related. Let's see how we can do this, in this video.

LCM and LCD

Don't worry, these really are the same number. When we compare our denominators, we find the lowest common multiple (LCM). We then use the LCM as the common denominator for both fractions. It's the lowest common denominator (LCD) now.

Worked Examples

Question 1

Find the lowest common denominator of $\frac{1}{2}$12 and $\frac{1}{7}$17.

To do this, we will look at the multiples of $2$2 and $7$7.

Fill in the table with the first ten multiples of $2$2.

$\times$×

$1$1

$2$2

$3$3

$4$4

$5$5

$6$6

$7$7

$8$8

$9$9

$10$10

$2$2

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

Fill in the table with the first ten multiples of $7$7.

$\times$×

$1$1

$2$2

$3$3

$4$4

$5$5

$6$6

$7$7

$8$8

$9$9

$10$10

$7$7

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

$\editable{}$

Hence, what is the lowest common denominator of $\frac{1}{2}$12 and $\frac{1}{7}$17?

Question 2

Find the lowest common denominator of $\frac{4}{5}$45 and $\frac{11}{12}$1112.

More than two fractions

If you are trying to find the lowest common multiple, and lowest common denominator, for more than two fractions, you use the same process. Instead of two rows of multiples, you'll have three. You need to find the lowest multiple in all three rows, as this next question demonstrates.

Question 3

Find the lowest common denominator of $\frac{3}{4}$34, $\frac{4}{5}$45 and $\frac{5}{8}$58.

Remember!

We are not changing the value of our fractions, just expressing one or more of them as equivalent fractions, so we have the same denominators.

Outcomes

NA4-4

Apply simple linear proportions, including ordering fractions