Prove there exist $a, b$ coprime such that $a|r, b|s$ and $lcm(r,s)=ab$ with $r, s\in\Bbb{N}$
106416
If $n,m \in \mathbb{N}$ then there are $c,d$ such that $cd = (m,n)$, $(c,d) = 1$ and $(m/c,n/d) = 1$.
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
95533
I need some help with a GCD and LCM's Problem
59462
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
10966
gcd and lcm from prime factorization proof
72672
Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
14809
Existence & uniqueness of solutions of linear congruences $\ cx\equiv b\pmod m$
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
71392
Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$