The primary target architectures of LFS are the AMD/Intel x86 (32-bit) and x86_64 (64-bit) CPUs. On the other hand, the instructions in this book are also known to work, with some modifications, with the Power PC and ARM CPUs.
The gain from building on a 64-bit system, as compared to a 32-bit system, is minimal. For example, in a test build of LFS-9.1 on a Core i7-4790 CPU based system, using 4 cores, the following statistics were measured:
Architecture Build Time Build Size
32-bit 239.9 minutes 3.6 GB
64-bit 233.2 minutes 4.4 GBAs you can see, on the same hardware, the 64-bit build is only 3% faster (and 22% larger) than the 32-bit build. If you plan to use LFS as a LAMP server, or a firewall, a 32-bit CPU may be good enough. On the other hand, several packages in BLFS now need more than 4 GB of RAM to be built and/or to run; if you plan to use LFS as a desktop, the LFS authors recommend building a 64-bit system.
The default 64-bit build that results from LFS is a “pure” 64-bit system. That is, it supports 64-bit executables only. Building a “multi-lib” system requires compiling many applications twice, once for a 32-bit system and once for a 64-bit system. This is not directly supported in LFS because it would interfere with the educational objective of providing the minimal instructions needed for a basic Linux system. Some of the LFS/BLFS editors maintain a multilib fork of LFS, accessible at https://www.linuxfromscratch.org/~thomas/multilib/index.html. But that's an advanced topic.