I originally made the mistake of assuming the three numbers were relatively prime and that N has to be a multiple of their product. (In that case the first 3 digit solution is n=123 and 123*124*125*77 = 1468900500.)
However if n is even then N need only be a multiple of half their product. The solution comes from the first number we can try:
100*101*102/2*285 = 146803500.
The first was basically a brute force solution using Excel. The second one didn't need to be but was a simple change.
Edited on May 13, 2014, 3:43 pm
Posted by Jer
on 2014-05-13 13:41:40