This has been discussed in another thread that I can’t find just now, but in a best/worst case scenario, if only one person turned out to the polls in each of the 11 most populous states, and those 11 people voted for Candidate A, and 100% of the people in the other 39 states all voted for Candidate B, then Candidate A would win.
I think I worked this out in a thread several months ago. If you assume that the total number of votes is exactly the same as it was in 2000, and that there are only two candidates, Candidate A can win enough states to win the electoral vote by one vote and Candidate B can get all the votes in the other states. Candidate A can then have won the electoral vote with less than 25 percent of the popular vote.
It depends on all sorts of factors, including how many major parties there are. (At times in the past there have been three or four major parties contesting presidential elections). But on one scenario you can win with none of the popular vote: if the candidate winning on election day dies between then and the day that the Electoral College votes, then a person can be elected who was not even on the ballot.