If R is a Principal Ideal Domain and let a and b be two non-zero elements of R. Prove that lcm(a,b)*gcd(a,b)=uab, where u is unity of R.
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
93686
In a UFD, lcm = product for coprimes: $\,(a,b)=1,\ a,b\mid c\Rightarrow ab\mid c$
587
Ideal Generated by the Union of Two Ideals
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
95533
I need some help with a GCD and LCM's Problem
147722
Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?
21288
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
45213
Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$
10966
gcd and lcm from prime factorization proof
41295
Divisibility, LCM and GCD for fractions (rationals)
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
23721
Prove that the Gaussian Integer's ring is a Euclidean domain