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
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