$R/(a) \oplus R/(b) \cong R/\gcd(a,b) \oplus R/\operatorname{lcm}(a,b) $
4648
Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
148108
Let $L=\operatorname{lcm}(o(a), o(b))$ and prove that $(ab)^L =e$.
6410
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
76048
Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$?
33338
Problem on $\operatorname{Hom}(\mathbb Z_6,R^*\oplus C^*)$
95533
I need some help with a GCD and LCM's Problem
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
21288
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
74809
GCD to LCM of multiple numbers
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
26110
Canonical isomorphism between $\mathfrak{so}(3)$ and $\mathbb R^3$ with vector cross product
59462
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
74187
$\operatorname{ord}(u)=r,\,\operatorname{ord}(v)=s$ $\,\Rightarrow\,\operatorname{ord}(uv)=rs\,$ if $\,r,s\,$ (co)primes