It's impossible to say without knowing the product, technology, codebase, etc. In some cases, yes, absolutely -- you would have three separate teams with three separate leads. In other cases, there isn't a reasonable way to split it up. Either way, there's no reason for the standup to last 45 minutes.

Whether the codebase should also be split up is another question that is impossible to answer in general. I can speak from experience though and say it's easy to have two teams work on the same large codebase when they're focusing on different areas, different projects, different priorities, etc. I've seen 3-4 different web teams work on the same website with the same underlying codebase without any issues at all because it was clear in advance that their work wasn't going to directly conflict in any way. It would've been hugely counterproductive to force all those people into a single standup and a single team.