Calculate the common denominator of 13/1387755 and 17/215873.



To find the common denominator of the fractions \( \frac{13}{1387755} \) and \( \frac{17}{215873} \), we need to calculate the **least common denominator (LCD)**. The LCD is the least common multiple (LCM) of the two denominators.

Given the denominators:
- \( 1387755 \)
- \( 215873 \)

### Step 1: Prime Factorization
To compute the LCM, we can use the prime factorizations of the numbers.

However, using the formula for the LCM of two numbers:
\[
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
\]
Where GCD stands for the greatest common divisor.

### Step 2: Compute the GCD of 1387755 and 215873
To find the GCD of \( 1387755 \) and \( 215873 \), we can apply the Euclidean algorithm. Let's calculate it step by step.

After computing, the GCD is found to be 1.

### Step 3: Compute the LCM
Now, since the GCD is 1, the LCM is simply the product of the two numbers:
\[
\text{LCM}(1387755, 215873) = \frac{1387755 \times 215873}{1} = 299562388215.
\]

Thus, the common denominator is **299,562,388,215**.

Let me know if you'd like any more details or have questions!

### Related Questions:
1. How do you simplify fractions with large denominators?
2. What are the steps for performing the Euclidean algorithm?
3. How does LCM differ from GCD in fraction calculations?
4. How can prime factorization help in finding the LCM?
5. Can two numbers always have a GCD of 1? What does it imply?

**Tip**: Always check if the GCD is 1 before calculating the LCM—this simplifies the process.

Calculate the common denominator of 13/1387755 and 17/215873.

Discover how to calculate the least common denominator (LCD) of the fractions 13/1387755 and 17/215873 using the least common multiple (LCM) and Euclidean algorithm. This step-by-step guide covers prime factorization and how to simplify fractions. Suitable for students in Grades 9-12.

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