private key is just a number so that is no the place you should look. what you should look into is the type of the curve and then the script types they create. since LTC is the exact copy of bitcoin, it also uses the same curve so the same number (private key) corresponds to the same public key. and since both use the same hash functions, they both come up with the same hash. and since they also use the same script structure (OP_HASH160 <20 byte> OP_EQUAL) then the scripts are also the same. the only thing different would be address format which is the base58 encoding (first byte) which doesn't matter at all.