It may help to understand that while 15 x 3.2V = 48V, you don't actually want exactly 48V. A 12V nominal battery is really 12.8V. So a 48V nominal battery is really 51.2V.
The other thing to understand is that you need your cells in 4S to build a 12V nominal. You need cells in 8S to build a 24V nominal, 12S for 36V nominal, and finally you need 16S to build 48V nominal.
If you wanted more capacity you could double it with twice the cells and then put the cells in 4S2P for a 12V, 8S2P for 24V, etc.
Incase you are not familiar, the "S" and "P" means series and parallel respectively.