Proving that $a \mathbb{Z} \cap b\mathbb{Z} = \operatorname{lcm}(a,b)\mathbb Z$
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
76100
Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
111555
Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$
71392
Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
100303
A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
40447
Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$.
147888
Show that $M=\bigcap_{\mathfrak{p}\in\operatorname{Spec}(R)}M_\mathfrak{p}=\bigcap_{\mathfrak{m}\in\text{Max}(R)}M_\mathfrak{m}$ for certain $M$.
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
21288
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
37346
If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$.