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Since the numbers 2, 5, 9, and 13 are pairwise relatively prime, their the least common multiple is equal to and therefore, the number is divisible by 2, 5, 9, and 13 if and only if is divisible by
The floor function is defined to be the greatest integer less than or equal to the real number .
In discrete math is well-known the fact that the number of numbers that do not exceed and are divisible by is equal to . Since each number is not divisible by 1170, between 1000 and 100,000 there are numbers which are divisible by 2, 5, 9, and 13.