number theory - is this a valid assertion? mn(m+n)(m-n)≡0 mod 6

[math_fan]

Given that I can prove \(\displaystyle mn(m+n)(m-n)≡0\ mod\ 6\)

I have a further value \(\displaystyle 4k^2 mn(m+n)(m-n)\)

Would I be correct in asserting that \(\displaystyle 4k^2 mn(m+n)(m-n)≡0\ mod\ 24k^2\)

Thanks