Agreed with the statements above, but let's also be clear. The war would have ended the same way - with a Japanese surrender to the United States. Consider the military position Japan was in by early August 1945, with no remaining air force or much of a navy to protect the home islands with. Vulnerable to all other kinds of bombing as well, as they had been for a year or more.
While historians consistently argue that the war ended sooner with a lower cost in lives, we will never know this for sure. The war ended not because of the atomic bombs, but because the Emperor of Japan told the military to lay down their weapons. Who is to say that the Emperor would not have done so after five more firebombings of Tokyo? How can we accurately say what was in his mind in early August before the bombs were dropped, or how strong his will was by that moment? We will never know, and at least part of why we argue that the bombs saved lives, in my opinion, is because we find a need to justify our actions as the only country ever to use nuclear weapons in war.