Find the least number n such that no factorial has n trailing zeroes or n+1 trailing zeroes or n+2 trailing zeroes. (153, 126, 624, 18)

Take the number 620: Number of zeroes in 620! are [620/5] + [620/25] + [620/125] = 124 + 24 + 4 = 152
Number of zeroes from 620! to 624! are the same.
In 625!, [625/5] + [625/25] + [625/125] + [625/625] = 156
Hence a number cannot have 153, 154 or 155 zeroes.
To arrive at the number 625, we have to note that in 625!, the number of zeroes increase by 4 because the total number of 5s increase by 4.