115 LearnersLast updated on July 9th, 2025
Least Common Denominator
Fractions that share the same denominator are said to have a common denominator. The least common denominator (LCD) is the smallest denominator that is common to the fractions given. Finding an LCD makes it easier to add, subtract, and compare fractions.
What is the Least Common Denominator
The least common denominator or LCD is the smallest number used as a common denominator for two or more fractions.
For example, take the fractions 34 and 56
Here, 4 and 6 are the denominators
To find the LCD, we need to list the multiples of the denominators 4 and 6 and find the least common multiple.
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28,….
The multiples of 6 are 6, 12, 18, 24, 30,...
Here, the LCD is 24
Now to add the fractions 34 and 56 , we need to make the denominators the same using the LCD
For 34 , multiply the numerator and denominator by 6.
34 = 3 x 64 x 6 = 1824
For 56, multiply the numerator and the denominator by 4.
56 = 5 x 46 x 4 = 2024
Now, both fractions have the same denominator for easy solution
34 + 56 = 3 x 64 x 6 + 5 x 46 x 4 = 1824 + 2024 = 3824 = 1912
Here 1912 is the simplified version of 3824
How to find an LCD?
To find the LCD, we use two basic methods:
- Listing Multiple Method
- Prime Factorization Method.
Now, let’s see how LCD is found using each method.
Listing Multiple Method
Here, we will keep listing the multiples of the denominators until we find the smallest common multiple.
For example, find the LCD of 158 and 164
Here, the denominators are 8 and 4
The multiples of 8 are 8, 16, 24, 32 ,...
The multiples of 4 are 4, 8, 12, 16,...
Therefore, we can say that LCD of 158 and 164 is 8
Prime Factorization Method
In this method, first, we break the denominators of each fraction given into its prime factors. Then we take the product of prime factors with the highest powers.
For example, 1412 and 56
Prime factorization of 12: 22 × 31
Prime Factorization of 6: 21 × 31
Product of prime factors with the highest powers: 22 × 31 = 2 × 2 × 3 = 12
Real Life Applications of Least Common Denominator
Whenever we deal with fractions in real-life, LCD is extremely helpful. We apply the concept of LCD in real-life situations like:
- Cooking and Baking: Adjusting portions involves adding or reducing. For example, sometimes you might have to add ¼ flour and ⅓ cup of sugar. To find their total, we need to find the LCD and then add.
- Comparing Discounts: To compare the discounts given by different vendors. If one store is giving a ½ discount and the others are giving only ¼, you can compare the discount rates
Common Mistakes and How To Avoid Them in the Least Common Denominator
Some students might find it difficult to calculate the LCD, which will lead to incorrect results. Let’s discuss some of the mistakes that can be made by students and the solutions to avoid them.
Mistake 1
Misunderstanding LCD with GCD
GCD is the Greatest Common Divisor that divides two or more numbers evenly. LCD is the least common multiple of the denominators of two or more fractions.
Mistake 2
Not listing the multiples correctly
Children might skip some numbers while listing the multiples, leading to an incorrect LCD. While listing the multiples, make sure that you double-check the multiples. For example, children might list the multiples of 4 and 6 as:
Multiples of 4 = 4, 8, 16, 20, …
Multiples of 6 = 6, 18, 24, 30,...
The correct way to list the multiples of given numbers is by multiplying the numbers starting from 1 until you find the common multiple.
The multiples of 4 and 6 will be:
Multiples of 4 = 4, 8, 12, 16, 20, …
Multiples of 6 = 6, 12, 18, 24, 30, ..
Mistake 3
Skipping prime factorization method
The prime factorization method is extremely useful when it comes to bigger complex numbers. Here, we divide the numbers into their prime factors and take the product of prime factors with the highest powers
Mistake 4
Choosing a random number as the LCD using the listing multiples method
Students might pick a random multiple as the LCD and try to solve the given fractions. Remember that LCD will always be the smallest common multiple of the denominators.
Mistake 5
Assuming that LCD is one of the denominators given
Always check if the given denominators are the same or not. If they are not the same, either use the listing multiples method or the prime factorization method to find the LCD.
Solved Examples for Least Common Denominator
Problem 1
Find (12/4 + 15/8) using the prime factorization method
The sum is 39/8
Explanation
Prime factorization of 4 = 22
Prime factorization of 8 = 23
Therefore, the LCD is 23 = 2 × 2 × 2 = 8
124 + 158 = 12 x 24 x 2 + 15 x 18 x 1 = 248 + 158 = 398
Problem 2
Subtract 95 from 105
The difference is 15
Explanation
Here, the denominators of the given fractions are the same. So the LCD is 5 itself. We can subtract them directly
105 - 95 = 15
Problem 3
Solve the mixed fractions 3 26 + 4 24
The sum is 476
Explanation
Since the given fractions are mixed fractions, so for conversion into improper fractions
3 26 = 206 and 4 24 = 184
The denominators are 6 and 4, let's prime factorize them to find the LCD.
Prime factorization of 4 = 22 × 1
Prime Factorization of 6 = 21 × 31
LCD = 22 × 31 = 2 × 2 × 3 = 12
206 = 20 x 26 x 2 = 4012
184 = 18 x 34 x 3 = 5412
Since the LCD is 12, we can now find the sum.
3 26 + 4 24 = 4012 + 5412 = 9412 = 476
Problem 4
What is (84 + 69) - (79 + 43) ?
The result is 59
Explanation
To find the difference, solve the brackets first
(84 + 69) = 8 x 94 x 9 + 6 x 49 x 4 = 9636
(79 + 43) = 7 x 19 x 1 + 4 x 33 x 3 = 199
(84 + 69) - (79 + 43) = 9636 - 199 = 2036 = 1018 = 59
Problem 5
John ate ¼ of a pizza and Max ate ⅙ of a pizza. Find out who ate more.
John ate more than Max
Explanation
To find out who ate more, we should determine the LCD of 4 and 6.
The LCD of 4 and 6 is 24
John: 14 = 1 x 64 x 6 = 624
Max: 16 = 1 x 46 x 4 = 424
FAQs on Least Common Denominator
1.Can -1 or any other negative number become LCD?
2.What are LCD and LCM?
3.Which methods are used to find the LCD?
4.How is it possible to find the LCD for mixed fractions?
5.What if the fractions have the same denominators?
6.How can children in Canada use numbers in everyday life to understand Least Common Denominator ?
7.What are some fun ways kids in Canada can practice Least Common Denominator with numbers?
8.What role do numbers and Least Common Denominator play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Least Common Denominator skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
