How do you find the least common denominator?

To find the least common denominator (LCD) of two or more fractions, follow these steps:

1. **List the denominators**: Identify the denominators of all the fractions involved.

2. **Find the prime factors**: Break down each denominator into its prime factors.

3. **Identify the highest power of each prime factor**: For each prime number that appears in the factorizations, take the highest power of that prime number that appears in any of the factorizations.

4. **Multiply these together**: Multiply these highest powers together to get the least common denominator.

Let's illustrate this with an example:

Find the least common denominator of \(\frac{1}{6}\) and \(\frac{1}{8}\).

1. **List the denominators**: 6 and 8.

2. **Find the prime factors**:
   - \(6 = 2 \times 3\)
   - \(8 = 2^3\)

3. **Identify the highest power of each prime factor**:
   - The prime factors are 2 and 3.
   - The highest power of 2 in the factorizations is \(2^3\).
   - The highest power of 3 in the factorizations is \(3^1\).

4. **Multiply these together**:
   \[
   \text{LCD} = 2^3 \times 3^1 = 8 \times 3 = 24
   \]

So, the least common denominator of \(\frac{1}{6}\) and \(\frac{1}{8}\) is 24.

Would you like any further details or have any questions?

Here are some questions you might ask next:
1. Can you show me another example of finding the least common denominator?
2. How do you add fractions with different denominators?
3. Can you explain how to subtract fractions with different denominators?
4. What is the process for multiplying fractions?
5. How do you divide fractions?

**Tip:** Practice prime factorization to quickly find the least common denominator, which helps simplify fraction operations.

Learn how to find the least common denominator (LCD) of fractions with a detailed step-by-step guide. This problem covers key mathematical concepts such as fractions and prime factorization. Suitable for students in Grades 4-6.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation