Greatest Common Divisor property: If $\gcd(a, b) = 1$ and $a | c$ and $b | c$, then $ab | c$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
71392
Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
94770
Greatest common divisor of two positive integers
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
110313
Prove that $\gcd(f(x),g(x)) = 1$.
75974
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?