Leave your calculator [multiple choice]

It is given that $x, y, z > 1$ and

$\begin{cases} \log_x w = 24 \\ \log_y w = 40 \\ \log_{xyz} w = 12 \end{cases} \implies w = \begin{cases} x^{24} \\ y^{40} \\ (xyz)^{12} \end{cases}$

$\begin{aligned} \implies x^{12}y^{12}z^{12} & = x^{24} = w \\ y^{12}z^{12} & = x^{12} = w^\frac 12 = y^{20} \\ z^{12} & = y^{8} = w^\frac 15 \\ z^{60} & = w \\ \implies \log_z w & = \boxed{60} \end{aligned}$