elementary set theory - Will $kappa_1, kappa_2, m$ cardinals. Given $kappa_1 leq kappa_2$. prove: $kappa_1 cdot m leq kappa_2 cdot m$

Will $\kappa_1, \kappa_2, m$ cardinals. Given $\kappa_1 \leq \kappa_2$. prove: $\kappa_1 \cdot m \leq \kappa_2 \cdot m$.

Hi, I would be happy if someone could help me with this. What I did until
now:I replaced the cardinals with sets: $|K_1|=\kappa_1$, $|K_2|=\kappa_2$, $|M|=m$. From what is given stems there is a injection $f:K_1→K_2$. Now I need to prove there is a injection $g:K_1⋅M \to K_2⋅M$, from multiplication of cardinals→ $g:K_1\times M → K_2\times M$. Now how do I show that?

I just started to learn this subject so would be happy to get a complete answer. Thanks!