The army sieging Minas Tirith as Macalaure references to is Karen Wynn Fonstads' Atlas of Middle-earth. Where she approximates this number of 45,000, I think she breaks it down to:
18,000 Haradrim
7,000 Variags from Khand
20,000 Orcs
Fonstad did not have access to the Letters of JRR Tolkien so there are some mistakes in it. However, it is one of the best Tolkien guides (if you're looking for a guide to the books) that is out there, and is highly recommended. Fonstad never just doesn't make up stuff, she's got textual support for it. I know where she came up with the 18,000 Haradrim, but I do not have the Atlas available and am still trying to figure out where the other 2 numbers come from. But as far as the Haradrim force on Pelennor fields, 18,000 seems to be a good approximation:
Quote:
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And if the Rohirrim at there onset were thrice outnumbered by the Haradrim alone, soon their case became worse, for new strength came now streaming to the field out of Osgiliath.~Battle of Pelennor Fields
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Theoden says he has '6,000' spears, thrice that amount, there's where the 18,000 Haradrim come from. Again this is just an approximation (even with the quote from the book...'if'), but I think it's a reliable one. I've never seen Fonstad's numbers disputed, as she always has a reasoning for them.
As far as those at the Morannon, the only clue I know of is that it would be greater than the force sent to siege Minas Tirith, because we are told that Sauron still hadn't sent his 'main army.' The 10 times as many as the force Aragorn sent out with seems reasonable.
Now in the movies, I've heard 250,000 were on the Pelennor Fields, and I can believe that seeing as it's a Jackson movie. The Morannon, as Mansun says did not seem to be very many, 10-20 thousand or so.