group theory – Show $(Gtimes H)/(Ktimes K’) cong G/Ktimes H/K’$ if $Klhd G$ and $K’lhd H$


As the title says, I want to show that $(Gtimes H)/(Ktimes K’) cong G/Ktimes H/K’$ if $Klhd G$ and $K’lhd H$.

I already showed that $Ktimes K’$ is a normal subgroup of $Gtimes H$ and I think that I should use the isomorphism theorem stating that if $A,B$ are groups and $f:Ato B$ is a homomorphism then $f(A)=A/text{ker}(f)$. But I can’t figure out how to go further. Can you help me to prove this problem?