$\gcd(ab,c)$ equals $\gcd(a,c)$ times $\gcd( b, c)$
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
71392
Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
87846
If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$
26861
$a+b=c \times d$ and $a\times b = c + d$