  In this paper, we prove that the multiplicative group of a unital
non-commutative Leavitt path algebra $L_K(E)$ and Cohn path algebra $C_K(E)$
contain a non-cyclic free subgroup, provided $K$ is a non-absolute field. We
also provide a description of the generators of free subgroups in term of the
graph $E$. Finally, we determine multiplicative groups of Leavitt path algebras
of some special types.
