However, what makes little sense is how there are so many Reapers in the first place? By my count, there are 12 races which the Reapers are currently trying to harvest. From the lore, that should result in 1 Reaper Dreadnaught, and 11 smaller Reapers.
We know an entire species is used to make a capital ship but we don't know how many is used to make the smaller reapers. Given their smaller size its likely a single species can make up many more than just one small reaper. Add that into the fact that the reapers have been doing this for over a BILLION years. That... that is a lot of time. It's possible the reapers have been around longer than our planet. We don't know for sure just how old they are. We only know they're ancient in every sense of the word.
What therefore confuses me is how do the Reapers have such great numbers, if each Harvest has them loosing more ships than they started with? Do they re-build the destroyed Reapers after they're done?
You're working off a misconception. The reapers do not lose more ships than they start with. Infact the reaper's do not often lose ships at all in the lore that we know of. There's like two instances we know of where theres destroyed reapers and these are OLD. Like, as old as our species. The fact that one of the only dead reapers we found is one that was wiped out that long ago is pretty telling of just how rare losses are for the reapers. Coincidentally the race that killed that single reaper did so at the cost of their lives and their planet as the weapon they used was so powerful it scarred their world. It was a kamikaze - all to take out one reaper.
Our cycle is special. Have you ever played the first game or talked to Javik from the ME3 DLC "From Ashes"? You get insight on this there.
The reaper harvest, traditionally, works this way:
1. Reapers signal Citadel, activating the relay to dark space.
2. Reapers take the Citadel and with it control of the entire relay network.
3. Reapers isolate the species of the cycle by disabling the relay network and systematically harvesting them world by world, system by system.
Our victory, our hope, our everything rides on the fact that the protheans altered the signal. The Citadel was never taken, though the Reapers tried (plot of ME1). Since we kept the Citadel we kept the relays. With the relays we kept connections. We are able to regroup, we are able to bring in resources, we are able to work together. How much chance do you think we have if every species was stuck in their system? We'd be at the mercy of the entire reaper armada that would be free to just waltz in full-force at their leisure.
The question here isn't how do the reapers have so many numbers but rather why don't they immediately take the Citadel instead of waiting months in ME3?
Also, it's possible the explanation is that they averaged a net positive and simply relied on the huge number of cycles (260,000 at most) to build up their numbers. However, that also begs the question of how they won in the first few cycles if they only had like 12 ships? Sure, maybe the Leviathans built a bunch to begin with, but considering how powerful those three guys were, an entire race should have been able to resist the Reapers. Maybe the first few cycles were just really easy or something?
The original cycle started with the Leviathan. The Intelligence (catalyst) was building a large network of resources and army for years before hand. The Leviathans never thought it a threat and just let it do its thing. They're above the concerns of lesser races. Apparently that didn't work out for them. The specifics of how it all went down though is never told. So... speculation.
It is reasonable to assume that the first races harvested (other than Leviathan) were primitive and unable to resist, though. Remember the pattern of synthetics killing organics? The whole point of the reapers in the first place? In the Mass Effect universe there exists a pattern where civilizations evolve to the point of making machines and then the machines turn on the creators and wipe them out. It would be relatively easy for the first reaper cycle to just wait for the more "advanced" civilizations to wipe themselves out.
They could harvest the ones that have no hope of fighting back and any that actually pose any form of threat can be left alone for a few years (relatively speaking) so that they wipe themselves out with their own creation. Perhaps the Catalyst can then swoop in and hack the synthetics that wiped them out and add them to it's arsenal. Either way, with or without the catalyst or its reapers, we organics are fated to be wiped out it seems. Yet life goes on.
Also, just so its clear, the Leviathan's didn't build the reapers. In case you thought they did with you "maybe Leviathans built a bunch" comment.