Is the formula $|G|=|\ker \varphi|.|\text{im}\space \varphi|$ connected to the formula $ab = \gcd(a,b) \cdot \operatorname{lcm}(a,b)$?
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
9393
Order of elements is lcm-closed in abelian groups
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
62959
How to find GCD, LCM on a set of numbers
74809
GCD to LCM of multiple numbers
102757
Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
127198
What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
121280
Proving that $a \mathbb{Z} \cap b\mathbb{Z} = \operatorname{lcm}(a,b)\mathbb Z$
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
145354
What is $\gcd(0,0)$?
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
147564
Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$