How many natural numbers below 1000 are divisible by at least one of 2, 3, 4, 6, 8 and 10?
Explanation:
Number of multiples of 2 till 1000 (excluding 1000) = 499
Number of multiples of 3 till 1000 (excluding 1000) = 333
Number of multiples of both 2 and 3 i.e., of 6 till 1000 = 166
Thus, total number of multiples of 2 or 3 = 499 + 333 – 166 = 666
These numbers will account for all multiples of 4, 6, 8 and 10 as well.
Hence, 666.
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