On 8 August 2017, President Trump threatened North Korea "with fire and fury and frankly power, the likes of which this world has never seen before." The 8th of August falls between the 6th of August, the anniversary of the US atomic bombing of Hiroshima, and 9 August, the bombing of Nagasaki. So whatever Mr. Trump intended to say, in that context of basic calendar what he did say was a threat against North Korea of "fire and fury" exceeding two smallish atomic bombs, a degree of "fire and fury" that would require a hydrogen bomb or several substantial fission bombs.
On 19 September 2017, in a prepared speech to the United Nations, Mr. Trump claimed great patience for the US but "if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea," presumably referring to destroying the Democratic Republic of North Korea as a functioning state but possibly meaning more — although it's hard to conceive of what that "more" could be unless he was thinking of North Korea as its human population (ca. 25.4 million people) and was threatening genocide, or had some idea that North Korea as a geographical entity could be destroyed by military action.
Whether the President of the United States on his own may legally order preventive genocide or even just state destruction by very-high high explosives is a question I now submit to readers expert in the law, but I will move from the initial calendar issue to a point from maps.
The City Distance website saith that Pyongyang, DPRK, is 684 km / 425 miles from Vladivostok in the Russian Federation, as the crow flies or fallout drifts, and about 810 km / 503 miles from Bejing, China. The Chinese border city of Dandong is about an even 100 miles from Pyongyang, 161 km; Dangong's population varies by how one defines the city, but just under a million people would give a fair idea.
It's not entirely clear how the governments of China and Russia would react to North Korea's being reduced — totally — to radioactive glass, but China has made it clear that it doesn't want to deal with large numbers of North Korean refugees, which would result from anything short of literal genocide; and it is a safe bet that both Russia and China would be very upset with radioactive fallout falling out on their territories, plus smoke, toxic gasses, and maybe a short-term nuclear winter or other climate change, including long-term warming.
Perhaps Mr. Trump should consider his reaction if China practiced some very hard-nose capitalism-by-other-means and nuked all Mexican maquiladoras 100 miles (161 km) or so south of the Rio Grande. Or he should consider Air Force General Buck Turgidson's description of Russian reaction upon seeing on their radar a wing of US B-52's entering their airspace: "[T]hey are going to go absolutely ape, and they're gonna strike back with everything they've got."
Call me a pessimist and/or an old softy, but I believe the Congress of the United State should specify — immediately and by a veto-proof majority — that the President of the United States is authorized to go nuclear with a counterattack to a nuclear strike on the US and can use subnuclear means of a wide variety to preempt an imminent attack of significant danger to the Republic and/or to large numbers of Americans. BUT: No preventive wars or nuclear strikes, especially on the scale of genocide. Zip, none, nada; and an order for such a nuclear strike is illegal, to be disobeyed by all people under the Uniform Code of Military Justice, and to result in the arrest of the Commander-in-Chief, as a person subject to the UCMJ.