14) Which of the following is a common denominator of \( 1 / 4 \) and \( 5 / 6 \) ? a) 8 b) 9 c) 12 d) 15

To find a common denominator for the fractions \( \frac{1}{4} \) and \( \frac{5}{6} \), we need to determine a number that both denominators (4 and 6) can divide into without leaving a remainder. This number is known as the **least common denominator (LCD)**. Let's examine the options: 1. **Option a) 8** - **4:** \( 8 \div 4 = 2 \) (no remainder) - **6:** \( 8 \div 6 = 1 \) with a remainder (not a whole number) - **Conclusion:** 8 is not a common denominator. 2. **Option b) 9** - **4:** \( 9 \div 4 = 2.25 \) (not a whole number) - **6:** \( 9 \div 6 = 1.5 \) (not a whole number) - **Conclusion:** 9 is not a common denominator. 3. **Option c) 12** - **4:** \( 12 \div 4 = 3 \) (no remainder) - **6:** \( 12 \div 6 = 2 \) (no remainder) - **Conclusion:** 12 is a common denominator. 4. **Option d) 15** - **4:** \( 15 \div 4 = 3.75 \) (not a whole number) - **6:** \( 15 \div 6 = 2.5 \) (not a whole number) - **Conclusion:** 15 is not a common denominator. **Therefore, the correct answer is:** **c) 12**