I'm trying to get a field that will show me the last time a lead was touched. This is defined as the date that something was recorded against the contact and should essentially be the last date between the following fields

Lead -  "Modified Time", 

Open Activity - "Modified Time" 

Closed Activity - "Modified Time" 

Email - "Date"

This field would very easily let me see if from a high level if leads have been followed up on in a timely manner. 

I have seen the various work-arounds suggested for manually updating the modified time, and that is pretty ridiculous. One can't get sales people to do these things no matter how much you try, and it is a waste of time. Especially when you buy the outlook plugins so you can make your workflow more efficient. 

I tried a formula so I could get the last date between activity and lead modified time. It's only half a solution .... but it doesn't update properly

Is there a way to programmatically do it with the API. We could run it once a day.