elearning BlogHow to Find Least Common Denominator

How to Find Least Common Denominator

how to find LCD with example

The least common denominator refers to the smallest same digit for the set of fractions. It is used in mathematics to perform addition, multiplication, and comparison of fractions. Dear students, you will learn in this blog, how to find LCD of the two fractions, and three fractions in a very simplified way.

After you skim this blog, you will get good suggestions and be able to address the problems. Let’s discuss how to get the lowest common denominator.

How to Find the LCD: Easiest Method

You will learn how to find the LCD step by step. You just need to follow these instructions

  • Consider the denominators of the two fractions
  • Perform prime factorization for both denominators
  • Identify the highest powers for both denominator's prime factors
  • Multiply these highest power prime factor values to determine the LCD of both fractions.

What is the Common Denominator of 81 and 6

Hopefully, you have learned what is the least common denominator of the fractions and how to find LCD of the two fractions. You should consider this example to understand the concept better.

Let’s discuss, what is the common denominator of 81 and 6. You will be able to solve this problem easily by following these steps

Prime Factors Identification

Prime Factors of 81=3×3×3×3=34\textbf{Prime Factors of 81} = 3 \times 3 \times 3 \times 3 = 3^4
Prime Factors of 6=2×3\textbf{Prime Factors of 6} = 2 \times 3

Highest Powers of Primes

21,342^1, 3^4

Multiplication of the Highest Powers

LCD=21×34=162\text{LCD} = 2^1 \times 3^4 = \mathbf{162}

What is the Common Denominator of 7/8 and 2/4

1.Prime Factors Identification

In the fractions

78&24\frac{7}{8} \quad \& \quad \frac{2}{4}

the denominators are 8 and 4. Now, let’s find their prime factors

8=2×2×2=238 = 2 \times 2 \times 2 = 2^3
4=2×2=224 = 2 \times 2 = 2^2

2.Highest Powers of Primes

The highest power is 23\text{The highest power is } 2^3

3.Multiplication of the Highest Powers

2×2×2=82 \times 2 \times 2 = 8
So, the common denominator of 78 & 24 is 8.\text{So, the common denominator of } \frac{7}{8} \text{ \& } \frac{2}{4} \text{ is } \mathbf{8}.

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