Cannot update apps - possible unknown Apple ID

I have 4 apps, all Apple products (Numbers, etc.) that were purchased with an ID I used but no longer have record for.

Apps will not update with the two I currently use.

It may have from the days when you only needed a login name instead of an email. When Apple made us all go to email, there were many who lost their apps. I seem to recall having Apple merge them a couple years later when they allowed their CSRs to help users migrate.

Is there any way to trace the account that purchased those apps?