## LCM(a,b,c) = n(a + b + c)

Show that

… if   $n \in N$,   there do not exist   $a, b \in N$   such that   $LCM(a,b) = n(a + b)$

… if   $n \in N$,   there exist infinitely many triples integers   $(a, b, c)$   such that
$LCM(a,b,c) = n(a + b + c)$