1023456798? ___________________________________________________ jeje I read it wrong. I read something like 2 and 9 divide it... I'm going to work it then...

No, that's not divisibly by $ 5$... it has to end in 0 for sure, since it's divisible by both 5 and 2.

1234857960

That is one... proof of minimality/way to come up with that?

1234759680. Solution in chinese: http://www.mathoe.com/dispbbs.asp?boardID=117&ID=16330&page=1

Can someone translate the solution please?

Suppose this number is $10N$, obviously we only need $7 \times 4\left| N \right.$,where $N$ used $1,2,3,4,5,6,7,8,9$ exactly once. If the left six digits is $123456$, $N\not \equiv 0(\bmod 4)$, contradiction; If the left five digits is $12345$, $4|N$ force the right two digits must be $68,76,96$, and so $N\not \equiv 0(\bmod 7)$, contradiction; If the left four digits is $1234$, $4|N$ force the right two digits must be $56,68,76,96$, suppose the right five digits is $M$, since $123400000\equiv 3(\bmod 7)$, so $M \equiv 4(\bmod 7)$. a)If $M = \overline {abc68} $, $100\overline {abc} + 68 \equiv 4(\bmod 7) \Rightarrow \overline {abc} \equiv 3(\bmod 7)$, so $\overline {abc} = 759$,$N = 123475968$; b)If $M = \overline {abc56} $, $100\overline {abc} + 56 \equiv 4(\bmod 7) \Rightarrow \overline {abc} \equiv 2(\bmod 7)$, no solution; c) If $M = \overline {abc76} $, $100\overline {abc} + 76 \equiv 4(\bmod 7) \Rightarrow \overline {abc} \equiv 6(\bmod 7)$, so $\overline {abc} = 895,958$, but $123495876 > 123489576 > 123475968$; d) If $M = \overline {abc96} $, $100\overline {abc} + 96 \equiv 4(\bmod 7) \Rightarrow \overline {abc} \equiv 3(\bmod 7)$, so $\overline {abc} = 857$, but $123485796 > 123475968$. So $10N = 1234759680$ is the best.