Question 58446
This problem is tough. I used a computer to help!

The least common multiple of 1*2*3...*18 = {{{2^4*3^2*5*7*11*13*17 = 12252240}}}

So, the answer is a multiple of 12252240.

I wrote a computer program to find all multiples of 12252240 that had 10 unique digits. The numbers that came back were 2438195760 3785942160 4753869120
and 4876391520.