Alternate proof for GCD × LCM = product
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
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 $d=\gcd(m,n)$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
14658
Deriving Chinese Remainder Theorem from gcd Bezout identity
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
50396
How can I show that $ab \sim \gcd (a,b) {\operatorname{lcm} (a,b)}$ for any $a,b \in R \setminus \{0\}$?
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
87926
Pumping Lemma for $L=\left\{0^i 1^{j} \mid \gcd(i,j) = 1\right\}$
48670
GCD in Gaussian integers.
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
21288
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
149249
Beginner: How to complete the induction case in a proof that all multiples are a product of the least common multiple
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
59856
Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$