query: A relation between the GCD and LCM of 3 numbers
positive_passages.docid: 65503
positive_passages.text: Identity involving LCM and GCD: $\frac{[a,b,c]^2}{[a,b][b,c][c,a]}=\frac{(a,b,c)^2}{(a,b)(b,c)(c,a)}$
negative_passages.docid: 10966
negative_passages.text: gcd and lcm from prime factorization proof
negative_passages.docid: 93686
negative_passages.text: In a UFD, lcm = product for coprimes: $\,(a,b)=1,\ a,b\mid c\Rightarrow ab\mid c$
negative_passages.docid: 119734
negative_passages.text: Why does prime factorization for LCM work?
negative_passages.docid: 21288
negative_passages.text: For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
negative_passages.docid: 1712
negative_passages.text: $ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
negative_passages.docid: 57281
negative_passages.text: Is Bezout's lemma enough to confirm the GCD of a number.
negative_passages.docid: 150909
negative_passages.text: GCD is MIN of Exponents of Prime Factors, LCM is MAX of Exponents of Prime Factors.
negative_passages.docid: 142693
negative_passages.text: $\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
negative_passages.docid: 76507
negative_passages.text: $\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
negative_passages.docid: 96535
negative_passages.text: Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?
negative_passages.docid: 6410
negative_passages.text: Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
negative_passages.docid: 71392
negative_passages.text: Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
negative_passages.docid: 37346
negative_passages.text: If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$.
negative_passages.docid: 87756
negative_passages.text: Order of a particular given permutation = LCM(order of all disjoint cycles) ?
negative_passages.docid: 48670
negative_passages.text: GCD in Gaussian integers.
negative_passages.docid: 125737
negative_passages.text: GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?