#Scala, 44 bytes#

    1.to(n(0)-1).filter(i=>n.exists(i%_==0)).sum

n is a List which contains of a first argument `N`, the rest are elements of `A`

Works by filtering out numbers where there doesn't exist at least one A of which i is a multiple, then summing.  Strictly speaking we should use `n.tail.exists` inside the closure, but as i is always less than N and therefore never a multiple of N the solution is still complete without this.