It is not that unusual to find that the smallest example of a number with certain properties turns out to be rather large. This is especially true if the specified properties implicitly build a certain factor structure into the required numbers. The smallest example can then turn out to be gigantic, although not necessarily hard to find if we exploit the given properties in our quest for the solution.An example of a number riddle of this kind is to find the smallest number that is five times a cube and three times a fifth power. The answer is