Lowest common denominator

key notes:

What is a Denominator?

  • In a fraction, the denominator is the number below the fraction line that shows how many equal parts the whole is divided into. For example, in the fraction 3/4, the denominator is 4.

What is a Lowest Common Denominator (LCD)?

  • The Lowest Common Denominator is the smallest number that can be used as the denominator for two or more fractions, allowing them to have the same denominator.
  • It’s the least common multiple (LCM) of the denominators.

Steps to Find the LCD:

  • Step 1: List the multiples of each denominator.
  • Step 2: Find the smallest multiple that is common in both lists.
  • Step 3: That smallest common multiple is the LCD.

Example 1:

  • For the fractions 1/4 and 1/6, find the LCD.
    • Multiples of 4: 4, 8, 12, 16, 20, 24…
    • Multiples of 6: 6, 12, 18, 24…
    • The smallest common multiple is 12, so the LCD is 12.

Example 2:

  • For the fractions 2/3 and 5/12, find the LCD.
    • Multiples of 3: 3, 6, 9, 12, 15, 18…
    • Multiples of 12: 12, 24, 36…
    • The smallest common multiple is 12, so the LCD is 12.

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 factorization for each number. 3 is a prime number. You do not need to factorize 3.
6 = 2 × 3

Repeat each prime factor the most number of times it appears in any of the prime factorizations 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 factorization 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 factorizations 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 1/2 and 5/8?

The denominators are 2 and 8. Find the lowest common multiple of 2 and 8.

Write the prime factorization for each number. 2 is a prime number. You do not need to factorize 2.

2
8 = 2 × 2 × 2

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

The most the factor 2 appears is three times.

So, multiply:

2 × 2 × 2 = 8
The lowest common multiple of 2 and 8 is 8.

The lowest common denominator of 1/2 and 5/8 is 8

Let’s practice!