Show that $\gcd(\gcd(a,b),b)=\gcd(a,b)$.
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
147802
Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
116175
Show that $\gcd(3k+2,5k+3)=1$