Some help with the following proof would be appreciated:

Prove that for all k,m,n in the set of Integers,

gcd(km, kn) = |k|gcd(m, n)

We have the following propositions already at our disposal.

*Every integer >= 2 can be factored into primes.

*Let m,n be in the Integers:

- gcd(m, n) divides both m and n

- unless m and n are both 0, gcd(m, n) > 0

- every integer that divides both m and n also divides gcd(m, n)