This Wiki page lists the Exchange Server 2013 / 2016 / 2019 and Cumulative Updates (CUs) build numbers with release dates and KB respectively.
More about Exchange 2013 Cumulative Updates (CUs) see MS Exchange Team Blog post Servicing Exchange 2013.
Exchange 2013, 2016 and 2019 Cumulative Updates include all Exchange binaries so you need to download only the latest CU.
You don't need to install Exchange Server RTM first.
Get-ExchangeServer | Select Name, AdminDisplayVersion
Get-Command Exsetup.exe | ForEach{$_.FileVersionInfo}
The below command will be given detailed information about the name, domain, edition, fqdn, server roles installed, site & admin display name.
Get-ExchangeServer | fl name, domain, edition, fqdn, serverrole, site, admindisplayversion
To check ExSetup.exe file version information on all Exchange servers remotely, use below command.
Get-ExchangeServer | Sort-Object Name | ForEach{ Invoke-Command -ComputerName $_.Name -ScriptBlock { Get-Command ExSetup.exe | ForEach{$_.FileVersionInfo } } } | Format-Table -Auto
In Exchange 2013 and Exchange 2016 we can also check build numbers in Exchange Admin Center (EAC).
In EAC click on "servers" category on the left side and then click on "servers" pane.
For update detail regarding earlier versions of Exchange Server (2003-2010), visit the Wiki page Exchange Server and Update Rollups Build Numbers