1. **State the problem:** We need to multiply the fractions $\frac{6}{13}$, $\frac{9}{77}$, and $\frac{11}{2}$ and simplify the result to its lowest terms. 2. **Write the multiplication of fractions formula:** When multiplying fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Multiply the numerators and denominators:** $$\frac{6}{13} \times \frac{9}{77} \times \frac{11}{2} = \frac{6 \times 9 \times 11}{13 \times 77 \times 2}$$ Calculate the numerator: $$6 \times 9 = 54$$ $$54 \times 11 = 594$$ Calculate the denominator: $$13 \times 77 = 1001$$ $$1001 \times 2 = 2002$$ So the fraction is: $$\frac{594}{2002}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 594 and 2002. Prime factorization: - $594 = 2 \times 3^3 \times 11$ - $2002 = 2 \times 7 \times 11 \times 13$ Common factors are $2$ and $11$. Multiply common factors: $$2 \times 11 = 22$$ Divide numerator and denominator by 22: $$\frac{\cancel{22} \times 27}{\cancel{22} \times 91} = \frac{27}{91}$$ 5. **Final answer:** The product in lowest terms is: $$\boxed{\frac{27}{91}}$$