$a|x$ and $b|x$ implies $\operatorname{lcm}(a,b)|x$
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
43000
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
50266
In the following figure prove that: $AK||BC$
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
148108
Let $L=\operatorname{lcm}(o(a), o(b))$ and prove that $(ab)^L =e$.
59856
Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
99376
Prove that If $m'$ is a common multiple of $s$ and $t$, then $m | m'$. Here $m$ is the LCM of $s$ and $t$.
25174
Solve for $A,B$: $\mathrm{LCM}(A,B)=168$, $\mathrm{HCF(A,B)}=12$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
102042
If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$