Let $a,b,cin{Z}^{+}.$ Prove:

$($a$)a*b*c*lcm(a,b,c)=gcd(a,b,c)*lcm(a,b)*lcm(b,c)*lcm(c,a)$

$($b$)$ lcm$(a,b,c)*gcd(a,b)*gcd(b,c)*gcd(c,a)=gcd(a,b,c)*a*b*c$