query: Let $m, n ∈\Bbb Z$ be nonzero integers, $d = \gcd(m, n)$ and $L = \operatorname{lcm}(m, n)$. Show that $dL = mn$.
positive_passages.docid: 21288
positive_passages.text: For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
negative_passages.docid: 78678
negative_passages.text: If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
negative_passages.docid: 60777
negative_passages.text: Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$
negative_passages.docid: 121280
negative_passages.text: Proving that $a \mathbb{Z} \cap b\mathbb{Z} = \operatorname{lcm}(a,b)\mathbb Z$
negative_passages.docid: 128710
negative_passages.text: Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
negative_passages.docid: 148108
negative_passages.text: Let $L=\operatorname{lcm}(o(a), o(b))$ and prove that $(ab)^L =e$.
negative_passages.docid: 50249
negative_passages.text: Pairs of numbers with a given LCM
negative_passages.docid: 124685
negative_passages.text: How to show $(mn)!$ is divisible by $(m!)^n$?
negative_passages.docid: 51858
negative_passages.text: Showing $\gcd(2^m-1,2^n+1)=1$
negative_passages.docid: 105666
negative_passages.text: What's an easy way to show that $GL(n,\mathbb C)$ is connected?
negative_passages.docid: 99376
negative_passages.text: Prove that If $m'$ is a common multiple of $s$ and $t$, then $m | m'$. Here $m$ is the LCM of $s$ and $t$.
negative_passages.docid: 10966
negative_passages.text: gcd and lcm from prime factorization proof
negative_passages.docid: 53364
negative_passages.text: dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
negative_passages.docid: 50396
negative_passages.text: How can I show that $ab \sim \gcd (a,b) {\operatorname{lcm} (a,b)}$ for any $a,b \in R \setminus \{0\}$?
negative_passages.docid: 88124
negative_passages.text: $M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
negative_passages.docid: 97196
negative_passages.text: $k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
negative_passages.docid: 72640
negative_passages.text: $(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$