how do you find common denominator of 1/20+1/68

To find the common denominator of the fractions \( \frac{1}{20} \) and \( \frac{1}{68} \), follow these steps:

### Steps:
1. **Find the Least Common Denominator (LCD):** The least common denominator is the least common multiple (LCM) of the denominators 20 and 68.
   
   To find the LCM of 20 and 68, we first find their prime factorizations:
   - \( 20 = 2^2 \times 5 \)
   - \( 68 = 2^2 \times 17 \)

   The LCM is the product of the highest powers of all prime factors:
   \[
   LCM(20, 68) = 2^2 \times 5 \times 17 = 340
   \]

2. **Rewrite each fraction with the common denominator (340):**
   - For \( \frac{1}{20} \), multiply both numerator and denominator by \( \frac{17}{17} \) to get:
     \[
     \frac{1}{20} = \frac{17}{340}
     \]
   - For \( \frac{1}{68} \), multiply both numerator and denominator by \( \frac{5}{5} \) to get:
     \[
     \frac{1}{68} = \frac{5}{340}
     \]

3. **Add the fractions:**
   \[
   \frac{17}{340} + \frac{5}{340} = \frac{22}{340}
   \]

4. **Simplify the result (if needed):**
   The greatest common divisor (GCD) of 22 and 340 is 2. So, divide both numerator and denominator by 2:
   \[
   \frac{22}{340} = \frac{11}{170}
   \]

Thus, \( \frac{1}{20} + \frac{1}{68} = \frac{11}{170} \).

Would you like further details or clarification?

Here are 5 related questions to practice:
1. How do you find the common denominator for \( \frac{1}{15} + \frac{1}{45} \)?
2. What is the sum of \( \frac{1}{12} + \frac{1}{16} \)?
3. How do you simplify \( \frac{24}{60} \)?
4. What is the LCM of 24 and 36?
5. How do you subtract fractions with different denominators?

**Tip:** Always factor the denominators first to efficiently find the least common denominator!

how do you find common denominator of 1/20 + 1/68

Learn how to find the least common denominator (LCD) of fractions 1/20 and 1/68. This step-by-step solution explains prime factorization, finding the LCM, and adding fractions with a common denominator. Suitable for students in Grades 5-7.

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