Proving lcm(m,n)=k using mZ and nZ intersection

[betty2301]

Homework Statement

prove:$mZ\cap nZ=kZ$
where lcm(m,n)=k

Homework Equations

The Attempt at a Solution

i can prove that kZ is a subset of mZ and nZ but i cannot prove further!
thx for ur help!

 

[Tedjn]

If x in mZ and nZ, x = am = bn for some integers a and b. So x is a common multiple of m and n. What is the relationship of x to k?