1. **State the problem:** Simplify the fraction $\frac{231}{1001}$ to its lowest terms and find the least common denominator (LCD) for the given options. 2. **Prime factorization:** To simplify, factor both numerator and denominator into primes. $$231 = 3 \times 7 \times 11$$ $$1001 = 7 \times 11 \times 13$$ 3. **Simplify the fraction:** Cancel common factors in numerator and denominator. $$\frac{231}{1001} = \frac{3 \times \cancel{7} \times \cancel{11}}{\cancel{7} \times \cancel{11} \times 13} = \frac{3}{13}$$ 4. **Answer:** The simplified fraction is $\frac{3}{13}$. 5. **Check options:** The simplified fraction matches option c) $\frac{3}{13}$. 6. **Find the LCD of all options:** Options denominators are 11, 31, 13, and 13. Prime factors: - 11 is prime - 31 is prime - 13 is prime LCD is the product of all distinct primes: $$\text{LCD} = 11 \times 31 \times 13 = 4433$$ **Final answers:** - Simplified fraction: $\frac{3}{13}$ - LCD of options: 4433