spending some of the coins nullifies address' balance. where does the remainder goes?
As you may know, transactions have inputs and outputs. The outputs give the addresses to which coins are being sent, and the inputs link back to outputs of the prior transactions that gave the coins to this transaction's sender, thus forming a chain. Anyone on the network can step along this chain to verify that all the coins in circulation legitimately got to their present owners.

To make it easier to verify the chain, the Bitcoin protocol has a rule that each input must spend all the coins that were in the output that it links to. (I am presuming that Litecoin is the same.) So if the smallest (or only) transaction to your address had
an output of 150 LTC, then you have to spend 150 LTC. But since you only really want to spend 45 LTC, your wallet gives the transaction a second output that sends the remaining 105 LTC back to you, as "change".

Rather than sending the change back to the same address that is spending the coins, some wallets choose to generate a new address and send the change there. I am not exactly sure why; perhaps it's to help obscure what addresses belong to whom, for privacy. But in any case, you should find that your wallet holds the private key to this new address. The 105  coins are still yours, they're just at a different address.