  Given two numerical semigroups $S$ and $T$ we say that $T$ is a multiple of
$S$ if there exists an integer $d \in \mathbb{N} \setminus \{0\}$ such that $S
= \{x \in \mathbb{N} \mid d x \in T\}$. In this paper we study the family of
multiples of a (fixed) numerical semigroup. We also address the open problem of
finding numerical semigroups of embedding dimension $e$ without any quotient of
embedding dimension less than $e$, and provide new families with this property.
