Say you have

a <- c(1,3,5,7,9)
b <- c(3,6,8,9,10)
c <- c(2,3,4,5,7,9)

A straightforward way to do the job is:

intersect(intersect(a,b),c)

More cleverly, and more conveniently if you have a lot of arguments:

Reduce(intersect, list(a,b,c))

The Reduce function is part of funprog {base}, which includes

Reduce(f, x, init, right = FALSE, accumulate = FALSE)
Filter(f, x)
Find(f, x, right = FALSE, nomatch = NULL)
Map(f, ...)
Negate(f)
Position(f, x, right = FALSE, nomatch = NA_integer_)

The other solution like this

intersectSeveral <- function(...) { Reduce(intersect, list(...)) } 
intersectSeveral(a, b, c)

intersect for multiple vectors in R