Find the product in lowest terms. \[ \frac{7}{3} \cdot \frac{5}{6} \]

To find the product of the fractions \(\frac{7}{3}\) and \(\frac{5}{6}\), you multiply the numerators together and the denominators together. So, \[ \frac{7}{3} \cdot \frac{5}{6} = \frac{7 \cdot 5}{3 \cdot 6} = \frac{35}{18} \] Next, we need to check if \(\frac{35}{18}\) can be simplified. The numerator \(35\) factors into \(5 \times 7\), and the denominator \(18\) factors into \(2 \times 3^2\). Since there are no common factors between \(35\) and \(18\), the fraction is already in its lowest terms. Thus, the product in lowest terms is \[ \frac{35}{18}. \]