Prove that: If $a,b,c \in \mathbb{N},$ then lcm (ca,cb) = c · lcm(a,b)
6410
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
111555
Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
93686
In a UFD, lcm = product for coprimes: $\,(a,b)=1,\ a,b\mid c\Rightarrow ab\mid c$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
2019
Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
21288
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
84422
$AB=BA$, $AC=CA$ we need to show $BC=CB$
58579
Can't understand a proof: Let $a,b,c$ be integers. If $a$ and $b$ divide $c$, then $lcm(a,b)$ also divides $c$
130513
LCM is associative: $\ \text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))$
99376
Prove that If $m'$ is a common multiple of $s$ and $t$, then $m | m'$. Here $m$ is the LCM of $s$ and $t$.