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20-07-2017
Mathematics

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How many positive integers not exceeding 1000 are not divisible by either 4 or 6?

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LammettHash LammettHash

20-07-2017

[tex]\left\lfloor\dfrac{1000}4\right\rfloor=250[/tex]

[tex]\left\lfloor\dfrac{1000}6\right\rfloor=166[/tex]

[tex]\left\lfloor\dfrac{1000}{\mathrm{lcm}(4,6)}\right\rfloor=\left\lfloor\dfrac{1000}{12}\right\rfloor=83[/tex]

[tex]250+166-83=333[/tex]

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