If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
75974
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
71392
Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
90480
Code for (a,b) with gcd(a,b)=1?
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$