elementary number theory - Modulus Cancellation Law

I'm trying to understand the proof for cancellation law in modulus which states that:

    ak = bk mod m


<=>     m | (a-b)k
                    since (k,m) = 1
<=>     m | (a-b)

<=>     a = b mod m

However, I don't understand why:

if $\,\gcd(k,m) = 1,\;$ then $\,m\mid(a-b)k \;\iff\; m\mid(a-b)$$

Can anybody help me please? :)