Minimal multiplicity of fiber components in abelian fibrations

An abelian fibration is a proper projective surjective map of complex varieties with general fiber an abelian variety. Consider a multiple fiber of an abelian fibration, and let $m_1,\mathrm{.}\mathrm{.}\mathrm{.},m_k$ be the multiplicities of its irreducible components. We prove that the minimum of $m_i$ is equal to their greatest common divisor $gcd(m_1,\mathrm{.}\mathrm{.}\mathrm{.},m_k)$