How to find the least common denominator of two fractions

The smallest number that is exactly divisible by the Denominator of a set of fractions. For example, the lowest common denominator (LCD) of ½, ¾ and 5/6 would be 12, as it the smallest number divisible by 2, 4 and 6.

What is the Least Common Denominator?

The least common denominator (LCD), also known as the lowest common denominator, is the smallest number that can be a common denominator for a set of fractions.

The LCD of two fractions, then, is the least common multiple of the denominators of the two fractions. To find the LCD of two fractions, you have to first find the least common multiple of the two fractions’ denominators.

How to Find the LCD of Two Fractions?

Whilst finding the least common denominator can seem complicated, it is actually a very simple process. There are 2 methods that you can use to find the LCD of two fractions.

Method 1

In the first method, the least common denominator of two fractions is found by figuring out the lowest of all of the possible common denominators.

For example:

Find the least common denominator of 1/4 and 1/6:

The denominators of these two fractions are 4 and 6. The multiples of 4 and 6 are:

Multiples of 4:4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …

Multiples of 6:6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …

From this list of multiples, we can clearly see that the least common multiple is 12. So, the least common denominator of these two fractions is 12.

Answer: The least common denominator of 1/4 and 1/6 is 12.

Method 2

To find the least common denominator using the second method, you must find the prime factors of the denominators. The second method of finding the LCD of two fractions can be laid out in these 4 easy steps:

1. Factor each of the denominators into its primes.
2. List all of the primes, noting down all of the matching primes.
3. Multiply the factors, and the product will be the lowest common multiple of the denominators.
4. The lowest common multiple of the denominators is the LCD of the two fractions.

For example:

Find the least common denominator of 1/8 and 1/12:

The denominators of these fractions are 8 and 12.

Now, we have to find the prime factorisations of these two denominators:

Prime factorisations of 8= 2 × 2 × 2

Prime factorisations of 12= 2 × 2 × 3

The most occurrences of the prime numbers 2 and 3 are 2 × 2 × 2 in 8 and 3 in 12.

Now we have to multiply all of the factors together.

2 × 2 × 2 × 3 = 24

Answer: The least common denominator of 1/8 and 1/12 is 24.

Teaching Resources on Fractions

We know that learning about fractions can be confusing for kids, this is why we have created a wide range of simple, engaging resources to help aid your students’ understanding. These resources include a variety of challenging worksheets, informative PowerPoints, complete lessons plans, classroom decorations, and more! All of our resources are made by teachers, for teachers, so you can be sure that you are getting the highest quality materials.

Boost your students’ understanding of fractions with these in-depth PowerPoints:

• Introduction to Fractions of Numbers PowerPoint: This PowerPoint is a fantastic tool for introducing your class to fractions. This colourful PowerPoint contains a detailed explanation of how to find half, a quarter, a third, three quarters, and two-thirds of different numbers. Kids will be given a step-by-step rundown of how to find fractions of different numbers, with tons of examples to aid their understanding.
• Year 6 Simplify Fractions and Common Denominators Maths Mastery PowerPoint: This PowerPoint is the perfect resource for getting your students to practice their knowledge of simplifying fractions. This PowerPoint is quick and easy to use, with a selection of challenging maths questions, such as ‘Simplify these fractions into the simplest form’. What’s more, this resource has a super bright and colourful design, with lots of images throughout, so kids will find it easy to stay engaged.

Once your students are comfortable using fractions, why not put their learning to the test with our vast selection of worksheets, activity sheets, and games:

• Funky Fraction Function Machine Worksheet: This worksheet is a super fun way for kids to challenge their knowledge of fractions. In this activity, kids will be presented with a selection of improper fractions that they must translate into mixed fractions by shading in the shapes provided.
• Finding Common Multiples: This worksheet is ideal for supplementing your teaching of how to find common multiples of fractions. Kids will have to work through 10 questions, listing the multiples of different numbers in order to find the lowest common multiple.

If you’re looking to spice up your classroom, check out these stunning fractions display resources:

• Fractions Wheels Display Posters
• Pizza Fraction Display Posters
• Fractions Display Pack
• Fraction Wall Large Display Poster

What is the least common denominator for two fractions?