I've been looking at the intersection of the ranges of real funtions which made me wonder about the functions of natural numbers.

When is the intersection of two or more sequences able to be described by a sequence and how do I find that sequence?

btw when I say intersection, I am refering to the intersection if sets (NOT where the fuctions are equal.

for example, the intersection of the sequences
a(n)=4n and a(n)=5n is a(n)=20(n)

how about polynomials, exponents, trigonomectic sequences, ect. Any thoughts?