  In the paper we prove that there exists a simultaneous reduction of
one-parameter family of $\mathfrak{m}_{n}$-primary ideals in the ring of germs
of holomorphic functions. As a corollary we generalize the result of A.
P\l{}oski \cite{ploski} on the semicontinuity of the \L{}ojasiewicz exponent in
a multiplicity-constant deformation.
