It isn't "low" budget, of course. We could also look at this that way: the complete trilogy was shot at the same time, so we could consider the total cost which is of 280 millions. Considering that we talk about three HUGE movies with a lot of costumes, sets, visual effects, long running times, many known actors and adapted froma successful book trilogy, I would say that it is not a "huge" budget neither.
Take in consideration that the cost to make all the three movies was not far from the cost of Avatar alone (which was of 237 millions). Here again, Avatar has a "modest" budget compared to movies like Pirates of the Caribbean 3 and 4 or Justice League which had exaggerated budgets and each cost more than the entire LotR trilogy (and I don't think anyone would say that they gave more than LotR).
So yeah, while I wouldn't call LotR a "low" budget movie, I wouldn't call it "high" budget neither.
And then, there's The Hobbit trilogy...
*Update*: Just checked another source, and apparently the LotR trilogy cost 260 millions. Actually I can be more accurate if I simply check each movie's individual budget and then I add up the numbers I would get the right amount but well... I'm lazy haha.
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