10. Let $m$ and $n$ be positive integers, and satisfy $24 m=n^{4}$. Then the minimum value of $m$ is . $\qquad$
10.54.

From $n^{4}=24 m=2^{3} \times 3 m$, we know
$$
m_{\min }=2 \times 3^{3}=54 \text {. }
$$