Question 66
On a board is written $\frac ab\cdot\frac cd\cdot\frac ef$, where $a,b,c,d,e,f$ are positive integers. Increasing $a$ by $1$ increases the expression by $3$. Increasing $c$ by $1$ in the original expression increases its value by $4$; increasing $e$ by $1$ in the original expression increases it by $5$. What is the least possible value of $bdf$? (N. Atakhanov)