I am looking for proof of this statement I encountered in a paper.
$\textbf{(Lucido’s Three Primes Lemma)}$- Let $G$ be a finite solvable group. If $p, q, r $ are distinct primes dividing |$G$|, then $G$ contains an element of order the product of two of these three primes.
I could not go much further with this. Any hint or references please.