combinatorics - Proving Kummer Theorem

Here is the theorem that way it was given to me...

Show that the highest power of a prime $p$ dividing the binomial coefficient
${n\choose m}$ equals the number of carries when $m$ is added to $n-m$, [EDIT] *in base $p$.

How do you go about proving this? I looked around and it seems the proof requires Legendre's formula but I'm not familiar with it. I'm not good with binomial coefficients and identities to begin with and I was given an example of this using binary code but I don't have any experience with that so I'm still lost.

If this is a duplicate question than I apologize in advance.