Lowest common denominator
Key Notes :
🧮 What is a Denominator?
The denominator is the bottom number of a fraction.
Example: In 3/4, 4 is the denominator.
🔹 What is a Common Denominator?
A common denominator is a number that two or more fractions share as their denominator.
Example: Fractions 1/4 and 1/6 → common denominator could be 12.
✨ Lowest Common Denominator (LCD)
The smallest number that is a common multiple of the denominators of two or more fractions.
Example: Fractions 2/3 and 3/4 → denominators 3 & 4 → LCD = 12 ✅
🔢 How to Find LCD (Step by Step)
Step 1: List the multiples of each denominator
3: 3, 6, 9, 12, 15…
4: 4, 8, 12, 16…
Step 2: Find the smallest multiple they share
Smallest common multiple = 12
✅ This is the LCD
✏️ Using LCD to Add or Subtract Fractions
Make all fractions have the same denominator (LCD).
Then, add or subtract the numerators only.
Example: 2/3+3/4 = 8/12+9/12 = 17/12
Multiply denominators if you can’t find LCD quickly (but may not be the lowest).
Always simplify the fraction at the end.
Practice with different numbers to get fast at spotting LCDs.
🎨 Fun Emoji Example
Fractions: 1/🍎 + 1/🍌
🍎 = 2, 🍌 = 3 → LCD = 6
Convert: 1/2 = 3/6,1/3 = 2/6
Add: 3/6+2/6 = 5/6🎉
Learn with an example
➡️ What is the lowest common denominator of 1/6 and 8/9 ?
The denominators are 6 and 9. Find the lowest common multiple of 6 and 9.
Write the prime factorisation for each number.
- 6 = 2 × 3
- 9 = 3 × 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 twice.
So, multiply:
2 × 3 × 3 = 18
The lowest common multiple of 6 and 9 is 18.
The lowest common denominator of 1/6 and 8/9 is 18.
➡️ What is the lowest common denominator of 2/5 and 7/10?
The denominators are 5 and 10. Find the lowest common multiple of 5 and 10.
Write the prime factorisation for each number. 5 is a prime number. You do not need to factorise 5.
5
10 = 2 × 5
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 5 appears is once.
So, multiply:
2 × 5 = 10
The lowest common multiple of 5 and 10 is 10.
The lowest common denominator of 2/5 and 7/10 is 10.
What is the lowest common denominator of 1/4 and 1/8?
The denominators are 4 and 8. Find the lowest common multiple of 4 and 8.
Write the prime factorisation for each number.
4 = 2 × 2
8 = 2 × 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 4 and 8 is 8.
The lowest common denominator of 1/4 and1/8 is 8.
Let’s practice!🖊️
