Let $ k \geq 2 $ and let $ ( L_{ n}^{ (k)} )_{ n \geq 2-k} $ be the $k-$generalized Lucas sequence with certain initial $ k $ terms and each term afterward is the sum of the $ k $ preceding terms. In this paper, we find all repdigits which are products of arbitrary three terms of $k-$generalized Lucas sequences. Thus, we find all non negative integer solutions of Diophantine equation $L_n^{ (k)}L_m^{ (k)}L_l^{ (k)} =a \left( \dfrac{ 10^{ d}-1}{ 9} \right)$ where $n\geq m \geq l \geq 0$ and $1 \leq a \leq 9.$
Categories: math.GM