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The type of North Korean missile with maximum reach should be its Taepodong-2 missiles, capable of reaching at least 6,000 kilometers, which enables it to hit targets in Alaska and Hawaii. Some say that it can even reach 10,000 kilometers.
The missiles with the longest range are Intercontinental ballistic missiles, which can travel more than a third of the Earth's circumference, and perhaps as far as half. In the latter case, you could say they have unlimited range, though I think the exact limits of the longest-range missiles are classified. In regards to North Korea, it is publicly estimated that they can send a missile as far as 2,500 miles (4000km), perhaps a little farther, but with limited accuracy or reliability. I've read some estimates that put this much higher at around 6,000 miles, far enough to barely reach the United States.