LCM and divisibility: $\,a,b\mid c\Rightarrow {\rm lcm}(a,b)\mid c$
58579
Can't understand a proof: Let $a,b,c$ be integers. If $a$ and $b$ divide $c$, then $lcm(a,b)$ also divides $c$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
130513
LCM is associative: $\ \text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))$
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
150909
GCD is MIN of Exponents of Prime Factors, LCM is MAX of Exponents of Prime Factors.
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
87756
Order of a particular given permutation = LCM(order of all disjoint cycles) ?
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
50249
Pairs of numbers with a given LCM
10966
gcd and lcm from prime factorization proof