The least integer greater than ${\log }_{2}15\cdot {\log }_{1/6}2\cdot {\log }_{3}1/6$ is

$\begin{array}{l}{\log }_{2}15\cdot {\log }_{1/6}2\cdot {\log }_{3}1/6\\ =\frac{\log 15}{\log 2}\cdot \frac{\log 2}{-\log 6}\cdot \frac{-\log 6}{\log 3}\\ ={\log }_{3}15\end{array}$