Show that $abc=[ab,bc,ca]*(a,b,c)=(ab,bc,ca)*[a,b,c]$ Let $a,b \in \mathbb N$. Show that
$$ abc=[ab,bc,ca](a,b,c)=(ab,bc,ca)[a,b,c] .$$
How would I prove this?

Fix a prime p. Show that the prime power p^k that divides each side is the prime power that divides abc.
Hence, we can even conclude that the expression is equal to abc
