At the bottom of the app's Settings screen each app shows something like Version 1.0.0 (24):

1.0.0 is the version name, a label for people. The update check ignores it.
(24) is the build number (Android “versionCode”, iOS “build”). These fields use this number.

Enter only the whole number, e.g. 24, not 1.0.0.24.

Where to find it

Rules

Set Latest only after that build is live in Google Play / the App Store; “Update” opens the store.
Build numbers must always go up. When the version name changes (e.g. to 2.0.0), keep counting: 2.0.0 should be build 25, not 1. iOS allows restarting at 1, but then the app would look older than before.
Android and iOS numbers are separate.
Test builds (build-apk.bat, the website's Mobile App page) don't count. Don't enter their numbers.
Minimum blocks every older app until it updates. Raise it only when old versions no longer work with the server. 0 = off.

Introduction