3. Among the 1000 natural numbers from 1 to 1000, the number of natural numbers that cannot be divided by 4 or 6 is ( )
A. 416
B. 584
C. 625
D. 667
3. $\mathrm{D}$ is determined by $\left[\frac{1000}{4}\right]=250,\left[\frac{1000}{6}\right]=166$.

Then, among the natural numbers from $1 \sim 1000$, there are 250 numbers divisible by 4, and 166 numbers divisible by 6.
The least common multiple of 4 and 6 is 12, and $\left[\frac{1000}{12}\right]=83$, so there are 83 natural numbers from $1 \sim 1000$ that can be divided by both 4 and 6. Thus, the number of the required natural numbers is $1000-166-250+83=667$. Therefore, the answer is D.