Greatest Common Divisor Divisibility
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
91921
Divisibility of $n\cdot2^n+1$ by 3.
97947
How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?
95533
I need some help with a GCD and LCM's Problem
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
9302
Questions about Divisibility of $2^n$ by $3$
113531
Repunit Divisibility
150528
Pythagorean triples $(a,b,c)$ and divisibility of $a$ or $b$ by $3$.
152878
calculate the gcd of $a+b$ and $p^4$
101940
If we know the GCD and LCM of two integers, can we determine the possible values of these two integers?
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
124890
Divisibility within a block of natural numbers
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$