Problem 622

Six natural numbers are written on the board, such that for any two $a$ and $b$ among them (where $b>a$), $\log _{a} b$ is an integer. What is the smallest value that the maximum of these numbers can take? The answer can be written in the form of a power of a number: $m^{n}$ is denoted as $\mathrm{m}^{\wedge} \mathrm{n}$.