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Proof that lcm(a,b) = ab/gcd(a,b)

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#elementary-number-theory #divisibility #integers #gcd-and-lcm #least-common-multiple
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Find the smallest number which leaves remainder $8,12$ when divided by $28$ and $32$.

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#number-theory #elementary-number-theory #least-common-multiple
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LCM of consecutive numbers

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#elementary-number-theory #least-common-multiple
196
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Equation between the greatest common divisor and the least common multiple

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#elementary-number-theory #arithmetic #gcd-and-lcm #least-common-multiple
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Coprime polynomials in $k[x,y]$ are also coprime in $k(y)[x]$

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#abstract-algebra #polynomials #least-common-multiple
228
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Function that turns GCD and LCM into intersections and unions?: $f(a)\cap f(b)=f(\gcd(a,b))$, $f(a)\cup f(b)=f(\operatorname{lcm}(a,b))$

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#number-theory #divisibility #gcd-and-lcm #least-common-multiple
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what is the smallest possible value of the other number

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#least-common-multiple
82
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Least common multiple of $\frac{n^2}{n^2 - 1}$ and $\frac{(n+1)^2}{ (n+1)^2 - 1 }$

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#least-common-multiple
75
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Is LCM of rationals used in higher math?

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#elementary-number-theory #rational-numbers #least-common-multiple
39
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Finding LCM of an expression

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#fractions #regular-expressions #least-common-multiple
128
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If $t_1\mid p-1$ and $t_2\mid q-1$, then $\text{lcm}(t_1,t_2) \leq \text{lcm}(p-1,q-1)$

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#number-theory #elementary-number-theory #least-common-multiple
278
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Finding numbers from LCM and HCF

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#number-theory #elementary-number-theory #gcd-and-lcm #least-common-multiple
140
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Prove $m=[a,b]\Longleftrightarrow \left(\frac{m}{a},\frac{m}{b}\right)=1$

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#elementary-number-theory #gcd-and-lcm #least-common-multiple
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Is $\mbox{lcm}(a,b,c)=\mbox{lcm}(\mbox{lcm}(a,b),c)$?

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#elementary-number-theory #discrete-mathematics #divisibility #least-common-multiple
374
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Self dual GCD/LCM identity in Landau's Elementary Number Theory

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#elementary-number-theory #divisibility #lattice-orders #gcd-and-lcm #least-common-multiple

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