2. Six natural numbers are written on the board, such that for any two $a$ and $b$ among them, $\log _{a} b$ or $\log _{b} a$ is an integer (the second logarithm does not necessarily exist). 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 $\mathrm{m}^{\wedge} \mathrm{n}$.

Answer: 65536 || $2 \wedge 16\left\|4^{\wedge} 8\right\| 16^{\wedge} 4 \| 256^{\wedge} 2$