In $\mathbb{Z}[X^2,X^3]$ the $lcm(X^2,X^3)$ and $gcd(X^2 \cdot X^3, X^2 \cdot X^2)$ do not exist
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
130944
Greatest common divisor of polynomials over $\mathbb{Q}$
68252
Chinese Remainder Theorem solvability for non-coprime moduli
52483
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
48452
Proof that $\gcd$ divides $\operatorname{lcm}$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
71392
Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
75970
$\mathbb Z[1/2]$ is not finitely generated?
66031
Rational Numbers - LCM and HCF