Find the lowest common denominator for the fractions shown. 19 51 85 255 O 17 O 4,335

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Learning Task: Understanding Common Denominators

**Question:**
Find the lowest common denominator for the fractions shown below.

![Fractions Image](Image_URL_Here)

**Fractions:**
\[
\frac{8}{51} \quad \text{and} \quad \frac{19}{85}
\]

**Multiple Choice Answers:**

- ○ 255
- ○ 17
- ○ 4,335

**Explanation:**
To find the lowest common denominator (LCD) for the fractions \(\frac{8}{51}\) and \(\frac{19}{85}\), follow these steps:

1. **Identify the denominators:** The denominators are 51 and 85.
2. **Factorize the denominators:** Find the prime factors of each denominator.
    - 51 = 3 × 17
    - 85 = 5 × 17
3. **Determine the LCD:** The LCD is the smallest number that both 51 and 85 can divide into without leaving a remainder. You can find this by taking the highest power of each prime factor involved:
    - Prime factors involved are: 3, 5, and 17.
    - LCD = 3 × 5 × 17 = 255

**Answer:**
The correct answer is:
- ○ 255
Transcribed Image Text:### Learning Task: Understanding Common Denominators **Question:** Find the lowest common denominator for the fractions shown below. ![Fractions Image](Image_URL_Here) **Fractions:** \[ \frac{8}{51} \quad \text{and} \quad \frac{19}{85} \] **Multiple Choice Answers:** - ○ 255 - ○ 17 - ○ 4,335 **Explanation:** To find the lowest common denominator (LCD) for the fractions \(\frac{8}{51}\) and \(\frac{19}{85}\), follow these steps: 1. **Identify the denominators:** The denominators are 51 and 85. 2. **Factorize the denominators:** Find the prime factors of each denominator. - 51 = 3 × 17 - 85 = 5 × 17 3. **Determine the LCD:** The LCD is the smallest number that both 51 and 85 can divide into without leaving a remainder. You can find this by taking the highest power of each prime factor involved: - Prime factors involved are: 3, 5, and 17. - LCD = 3 × 5 × 17 = 255 **Answer:** The correct answer is: - ○ 255
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