iTunes could not back up the iPhone “XXX” because there is not enough free space on this computer to save the backup

I believe many people out there are having sam issue right now.

I purchased iphone 6s (64GB) last week, and my old phone is 5s (32GB) .

As all of us do, we try to backup and restore into the new phone.

However, as I do so itunes showed

iTunes could not back up the iPhone “XXX” because there is not enough free space on this computer to save the backup

I have tried this iPhone、iPad、または iPod touch を iTunes でバックアップできない場合 - Apple サポート

and all sort of other methods provided online.

In addition, I bought 50GB icloud for trying to backup via icloud, still didnt help at all

From what I have searched, many people are same situation when trying to backup their phone to their new phone.

Do any people out here have way to backup without doing the troubleshoot procedures from apple cause it does not help at ALL.