if m,n are positive integers such that; $3m+n=3 lcm(m,n)+gcd(m,n)$
111555
Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
8160
What is $\gcd(0,a)$, where $a$ is a positive integer?
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
70006
$a,b,m,n$ be positive integers such that g.c.d.$(a,b)=1$ and $a^m+b^m|a^n+b^n$ , then $m|n$?
76652
Finding the maximum $lcm$ of a set of numbers with sum $n$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
14783
A Number Theory problem (GCD)
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
45213
Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.