Hi Sue! Your question is a two-parter, as I see it. First, what program will work in Linux, Android, and iPhone to read and write changes to a spreadsheet. Part two is about networking... how can these devices all access the same file (not each device storing a separate copy).
Part One is I think fairly easy. When you create spreadsheets in LibreOffice... save them as Microsoft Excel files instead of the LibreOffice .ods format. I strongly prefer the older Microsoft format (.xls instead of .xlsx). I think that the older .xls is better compatible with LibreOffice. Also, do not use macros in your spreadsheets. Formulas should be fine between devices, but macros can be a problem. Once your spreadsheet is in Microsoft format, you can use a free Microsoft Excel app on Android and iPhone.
Part Two is the more tricky problem, or it can be. You can set up a home network so that the master spreadsheet file is on your Linux computer, and that file (or folder) would be shared to your other devices. But network sharing can be a real pain, and especially when you throw Apple into the mix.
I think the more simple solution would be to use a Dropbox cloud storage for your spreadsheets. You can have up to 2GB of storage space for free, and Dropbox can work with Linux, Android, and iPhone. The apps for Android/iPhone should be fairly easy to setup after you create an account. But with Linux you have a couple of options.
This article describes installing Dropbox in Ubuntu (should be same for Mint)... and this creates a special folder that is automatically synchronized with the Dropbox cloud, so it would always be current for your Android/iPhone devices to use. This is probably what you want. I only mention another option because I use Dropbox (only rarely) but I do not install their software.... I just go to their website and log in, and then I manually copy/delete files in my storage space there. It works well enough for me this way, but it's on me to keep my files current. I don't share with other devices of my own... I share with other family members (genealogy data).
With Linux, there is always more than one way to do anything. I think Dropbox is about the easiest way to go, or the easiest that I can think of off the top of my head. And the 2GB limit should be plenty for spreadsheets... it's photos and videos that get people to buy more storage space.
Cheers