Answer
666,667
Work Step by Step
Since we want to find the positive integers less than 1,000,000, so we have 999,999 numbers.
Therefore $\left \lfloor{\frac{999,999}{4}}\right \rfloor$ = 249,999 numbers that are divisible by 4, and $\left \lfloor{\frac{999,999}{6}}\right \rfloor$ = 166,666 numbers that are divisible by 6. However, numbers can be
divisible by both 4 and 6; namely those divisible by 12, the least common multiple of 4 and 6. There are $\left \lfloor{\frac{999,999}{12}}\right \rfloor$ = = 83,333 such numbers.
We want to exclude these from the 999,999 numbers. Using the principle of inclusion-exclusion, answer is
999,999 - (249,999 + 166,666 - 83,333) = 666,667.
