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How to manually figure out which linker to use with a given libc file and given binary?

Background is I am looking at an old CTF challenge from pico-CTF. You do have the Makefile, the binary itself and the correspondig libc file available. However the binary will not run on my machine but abort with a segmentation fault. According to a writeup I have available this is due to the mismatched linker (ld-linux-xxxxx.x.so) on the local machine. In the writeup he then uses a different ld-file and everything is fine. So I would like to know how can you figure out which ld-file you need to use. I know you can then use patchelf with the --set-interpreter option to run that binary normally but how to know which linker to use blows my mind. Would be great if anyone can give me some insight into that or at least point me to some link where I can readup on that. so far I havent found anything useful yet.