  This contribution presents all possible solutions to the Diophantine
equations $F_k=L_mL_n$ and $L_k=F_mF_n$. To be clear, Fibonacci numbers that
are the product of two arbitrary Lucas numbers and Lucas numbers that are the
product of two arbitrary Fibonacci numbers are determined herein. The results
under consideration are proven by using Dujella-Peth\"o lemma in coordination
with Matveev's theorem. All common terms of the Fibonacci and Lucas numbers are
determined. Further, the Lucas-square Fibonacci and Fibonacci-square Lucas
numbers are given.
