Which is correct

[gwendolinest]

I saw the following random quote:

"I feel that if a person has problems communicating the very least he can do is to shut up"
Tom Lehrer


is it valid to say "the very least he can do is shut up" (note the absense of 'to') ?

I wouldn’t use “to” there. I’d just say “the very least he can do is shut up”.

BTW, the correct spelling of the word I underlined in the quote above is absence.

()

[ExK]

thank you teachers! I still have some taxing questions, but I'll ask when I've returned from overseas!

[MikeNewYork]

I saw the following random quote:

"I feel that if a person has problems communicating the very least he can do is to shut up"
Tom Lehrer


is it valid to say "the very least he can do is shut up" (note the absense of 'to') ?

Both versions would be acceptable, but I would use the "to". "To shut up" is a predicate nominative. If the sentence were reversed "To shut up is the very least he can do" the "to" would be required.