The exercise asks you to find the least common denominator (mindste fællesnævner) for two sets of fractions:

1. $\frac{1}{3}, \frac{1}{5}$
2. $\frac{2}{7}, \frac{2}{3}, \frac{1}{5}$

Let's solve for both sets:

1. Finding the least common denominator for $\frac{1}{3}, \frac{1}{5}$

• The denominators are 3 and 5.
• The least common denominator (LCD) is the least common multiple (LCM) of 3 and 5.
• Since 3 and 5 are prime numbers, their LCM is simply $3 \times 5 = 15$.
• Therefore, the LCD for $\frac{1}{3}$ and $\frac{1}{5}$ is 15.

2. Finding the least common denominator for $\frac{2}{7}, \frac{2}{3}, \frac{1}{5}$

• The denominators are 7, 3, and 5.
• We need to find the LCM of 7, 3, and 5.
• Since all three numbers are prime, their LCM is $7 \times 3 \times 5 = 105$.
• Therefore, the LCD for $\frac{2}{7}, \frac{2}{3}, \frac{1}{5}$ is 105.

Final Answers:

• The LCD for $\frac{1}{3}, \frac{1}{5}$ is 15.
• The LCD for $\frac{2}{7}, \frac{2}{3}, \frac{1}{5}$ is 105.

Would you like further details or have any questions about these steps?

Here are some additional questions to expand your understanding:

1. How do you find the least common denominator for more than two fractions?
2. Why are prime numbers important when finding the least common multiple?
3. How do you convert fractions to have a common denominator?
4. Can you solve for the least common denominator when one denominator is not a prime number?
5. What happens if two or more denominators share common factors?

Tip: When finding the least common denominator, always factorize the denominators first to simplify the process.