Only three were made. The process of making fissionable material in those days was slow.
There was a third plutonium "pit" waiting at Los Alamos, which would have made for the fourth atomic bomb, and it was already packaged and prepared for shipment to Tinian. But it never left the facility because Truman signed an order on the 12th of August that the bombing was to stop.
U-235 was (and still is) slow to produce but Pu-239 was not. At one juncture the plant at Oak Ridge was burning one-seventh of all the commercial electricity produced in the US to power all the centrifuges and gaseous diffusers they were running, and they only created enough U-235 for the one device. On the other hand, once the two atomic reactors Groves had had built in Washington were up to full speed (in about December of '45), they produced enough Pu-239 each month for four more bombs.
The order written by FDR (not Truman) stated that until Japan capitulated, they were to continue dropping atom bombs on Japan as soon as they became available. So if Japan hadn't surrendered, there was the potential that by January of 1946, the US could have been nuking one Japanese city a week like clockwork.
Or they could have turned the show over to Curtis LeMay. He had just inherited 10,000 bombers from the War in Europe, which gave him the firepower to run hundreds of napalm sorties on Japan, every day, seven days a week.