Question

How many positive integers less than 1000 are divisible by exactly one of 7 and 11?

Answer 1

994/7(number of multiples of 7 smaller than 1000) + 990(number of multiples of 11 smaller than 1000) - 924/(lcm of 7 and 11) (number of multiples of 77 smaller than 1000) = 142+90-12
                   = 220

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