Lowest common denominator

Key notes:

📘 What is a Denominator?

  • In a fraction, the denominator is the bottom number.
  • It tells us how many equal parts the whole is divided into.
    • Example: In 3/4, 4 is the denominator.

📘 What is the Lowest Common Denominator (LCD)?

  • The Lowest Common Denominator is the smallest number that is a common multiple of two or more denominators.
  • It is used to make the denominators the same when adding, subtracting, or comparing fractions.

📘 Why is LCD Important?

  • To add or subtract fractions, the denominators must be the same.
  • Using the LCD helps keep the numbers as small as possible for easier calculation.

🧮 How to Find the LCD:

Step 1: List the multiples of each denominator.

Step 2: Find the smallest common multiple.

Step 3: Use the LCD to rewrite the fractions.

📍 Example:

Find the LCD of 1/6 and 1/8:

  • Multiples of 6: 6, 12, 18, 24, 30, 36, …
  • Multiples of 8: 8, 16, 24, 32, 40, …
  • Common multiple: 24
  • ✅ LCD = 24

So,
1/6 = 4/24
1/8 = 3/24

Now you can easily add:
1/6 + 1/8 = 4/24 + 3/24 = 7/24

✏️ Tip:

  • LCD is the LCM (Lowest Common Multiple) of the denominators.
  • You can also find it using prime factorization or the LCM method.

Learn with an example

🔥What is the lowest common denominator of 2/3 and 5/6?

The denominators are 3 and 6. Find the lowest common multiple of 3 and 6.

Write the prime factorisation for each number. 3 is a prime number. You do not need to factorise 3.

3
6 = 2 × 3

Repeat each prime factor the most number of times it appears in any of the prime factorisations above.

The most the factor 2 appears is once.

The most the factor 3 appears is once.

So, multiply:

2 × 3 = 6
The lowest common multiple of 3 and 6 is 6.

The lowest common denominator of 2/3 and 5/6 is 6.

🔥What is the lowest common denominator of 5/8 and 1/4?

The denominators are 8 and 4. Find the lowest common multiple of 8 and 4.

Write the prime factorisation for each number.

8 = 2 × 2 × 2
4 = 2 × 2

Repeat each prime factor the most number of times it appears in any of the prime factorisations above.

The most the factor 2 appears is three times.

So, multiply:

2 × 2 × 2 = 8

The lowest common multiple of 8 and 4 is 8.

The lowest common denominator of 5/8 and 1/4 is 8.

What is the lowest common denominator of 1/3 and 1/12?

The denominators are 3 and 12. Find the lowest common multiple of 3 and 12.

Write the prime factorisation for each number. 3 is a prime number. You do not need to factorise 3.

3
12 = 2 × 2 × 3

Repeat each prime factor the most number of times it appears in any of the prime factorisations above.

The most the factor 2 appears is twice.

The most the factor 3 appears is once.

So, multiply:

2 × 2 × 3 = 12
The lowest common multiple of 3 and 12 is 12.

The lowest common denominator of 1/3 and 1/12 is 12.

Let’s practice!