Three, (Full marks 20 points) Try to write down 5 natural numbers, such that the larger of any two of these numbers can be divided evenly by their difference.

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Three, 1680, 1692, 1694, 1695, 1696 are 5 numbers that meet the conditions. (Note: The answer is not unique)
The above 5 numbers can be found through the following steps:
First step: $2,3,4$ are three numbers that meet the requirements.
Second step: Let $a, a+2, a+3, a+4$ be four numbers that meet the conditions, then $a$ can be divided by $2,3,4$. Take $a=12$, to get four numbers that meet the conditions $12,14,15,16$.

Third step: Let $b, b+12, b+14, b+15, b+16$. Take the least common multiple of $12,14,15,16$ as $b$. That is, $b=1680$, to get five numbers that meet the conditions $1680,1692,1694,1695,1696$.