query: Proof $\displaystyle \text{lcm}(x,y)=\frac{|x\cdot y|}{\text{gcd}(x,y)}$
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: 2626
negative_passages.text: Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$
negative_passages.docid: 49294
negative_passages.text: prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
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: 125737
negative_passages.text: GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
negative_passages.docid: 65503
negative_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: 67660
negative_passages.text: Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
negative_passages.docid: 110313
negative_passages.text: Prove that $\gcd(f(x),g(x)) = 1$.
negative_passages.docid: 41295
negative_passages.text: Divisibility, LCM and GCD for fractions (rationals)
negative_passages.docid: 147802
negative_passages.text: Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
negative_passages.docid: 92630
negative_passages.text: How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
negative_passages.docid: 147902
negative_passages.text: Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
negative_passages.docid: 59856
negative_passages.text: Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$
negative_passages.docid: 52642
negative_passages.text: Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$
negative_passages.docid: 69715
negative_passages.text: Proving $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$
negative_passages.docid: 1713
negative_passages.text: number theory $\gcd(a,bc)=\gcd(a,c)$
negative_passages.docid: 6410
negative_passages.text: Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]