GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
71392
Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
41295
Divisibility, LCM and GCD for fractions (rationals)
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
150909
GCD is MIN of Exponents of Prime Factors, LCM is MAX of Exponents of Prime Factors.
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
145354
What is $\gcd(0,0)$?
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
135086
GCD of two numbers divided by their greatest common divisor is 1
45213
Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$