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Question Number 14440 by christine last updated on 31/May/17

Answered by prakash jain last updated on 31/May/17

$$\mathrm{number}\mathrm{of}\mathrm{integer}1⩽n⩽100$$$$\mathrm{divisible}\mathrm{by}4=\lfloor \frac{100}{4}\rfloor =25$$$$\mathrm{divisible}\mathrm{by}6=\lfloor \frac{100}{6}\rfloor =16$$$$\mathrm{divisible}\mathrm{by}\mathrm{by}4\mathrm{and}6=\lfloor \frac{100}{12}\rfloor =8$$$$\left(12\mathrm{is}\mathrm{lcm}\mathrm{for}4\mathrm{and}6\right)$$$$------$$$$\mathrm{number}\mathrm{of}\mathrm{integer}1⩽n⩽100$$$$\mathrm{divisible}\mathrm{by}4\mathrm{or}6=25+16-8=33$$$$$$$$\mathrm{number}\mathrm{of}\mathrm{integers}\mathrm{not}\mathrm{divisible}$$$$\mathrm{by}4\mathrm{or}6=100-33=67$$

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