$\gcd(n,m)=10$, and $\text{lcm}(n,m)=100$
59856
Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$
45213
Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
57281
Is Bezout's lemma enough to confirm the GCD of a number.
51858
Showing $\gcd(2^m-1,2^n+1)=1$
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
112486
Bounds on a sum of gcd's
74809
GCD to LCM of multiple numbers
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
52483
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
150185
Let $d=GCD(n^2+5,n^3-5n^2+6n)$ show that $d|630$
90480
Code for (a,b) with gcd(a,b)=1?
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$