Say the first monkey takes $8x$ bananas, keeping $6x$ and giving $x$ to each of the others; the second takes $8y,$ keeping $2y$ and giving $3y$ to each; the third takes $24z,$ keeping $2z$ and giving $11z$ to each. All divisions are whole numbers exactly when $x,$ $y,$ $z$ are positive integers. The final amounts are $6x + 3y + 11z,$ $x + 2y + 11z,$ and $x + 3y + 2z.$

The ratio $3 : 2 : 1$ says the first amount is triple the third and the second is double the third: $$\begin{aligned} &6x + 3y + 11z = 3(x + 3y + 2z) \\ &\quad \Longrightarrow\quad 3x + 5z = 6y, \end{aligned}$$ $$\begin{aligned} &x + 2y + 11z = 2(x + 3y + 2z) \\ &\quad \Longrightarrow\quad x + 4y = 7z. \end{aligned}$$ Substituting $x = 7z - 4y$ into the first equation gives $26z = 18y,$ so $9y = 13z.$ Thus $y = 13n$ and $z = 9n$ for a positive integer $n,$ and then $x = 63n - 52n = 11n.$

The total is $8x + 8y + 24z$ $= (88 + 104 + 216)n$ $= 408n,$ least when $n = 1:$ the answer is $408.$