Is there a name for the least exponent $e$ such that a power of an integer is divisible by another?

Question

Say the primes dividing $m$ also divide $n$. Is there a name for the least exponent $e$ such that $m | n^e$?

I can write that explicitly using the prime factorizations of $m$ and $n$, but am wondering whether this exponent has a name, is a famous arithmetic function, ...