There are n horses. At a time only k horse can run in the single race. How many minimum races are required to find the top m fastest horses? Please explain your answer.

PS:There is no timer.

This was asked and not answered at [math.stackexchange](http://math.stackexchange.com/questions/209790/how-to-find-a-total-order-with-constrained-comparisons). The $n = 25, k = m = 5$ case was a Google interview question and there are various answers on the web. But I am not sure what should be the right answer for this. Any ideas?