Question

Prove $\frac{ab}{m} = \gcd(a,b)$ when $m=\operatorname{lcm}(a,b)$, for all natural numbers $a$ and $b$.

score 83 · Answer 1 · 2018-11-14 10:42:55

83

Views

Prove $\frac{ab}{m} = \gcd(a,b)$ when $m=\operatorname{lcm}(a,b)$, for all natural numbers $a$ and $b$.

Published on 14 Nov 2018 - 10:42

score 123 · Answer 2 · 2018-11-16 18:31:54

123

Views

Is this approach valid for using least common multiple to establish Bertrand's postulate

Published on 16 Nov 2018 - 18:31

score 34 · Answer 3 · 2018-11-18 17:08:29

34

Views

Coprimality of elements of set of numbers with maximum LCM and given fixed sum.

Published on 18 Nov 2018 - 17:08

score 142 · Answer 4 · 2018-12-04 21:13:11

142

Views

Upper bound for a ratio of two least common multiples

Published on 04 Dec 2018 - 21:13

score 201 · Answer 5 · 2018-12-06 15:35:29

201

Views

Product of gcd and lcm for multivariate polynomials

Published on 06 Dec 2018 - 15:35

score 35 · Answer 6 · 2018-12-07 11:19:00

35

Views

If $g = gcd(a,b)$ prove (a,b)=(g). Furthermore, if $k = lcm(a,b)$ prove that $(a)\cap(b) = (k)$

Published on 07 Dec 2018 - 11:19

score 66 · Answer 7 · 2018-12-07 22:22:51

66

Views

Show that $\alpha = (1 2 3)(2 3 4)(5 6 7)(7 8 9 10)$ has order $10$ in $S_n$ $(n\geq10)$.

Published on 07 Dec 2018 - 22:22

score 137 · Answer 8 · 2018-12-09 08:56:02

137

Views

Using least common multiple to prove there exists a prime between $2x$ and $3x$

Published on 09 Dec 2018 - 8:56

score 47 · Answer 9 · 2018-12-15 11:30:01

47

Views

Is this proof acceptable?

Published on 15 Dec 2018 - 11:30

score 66 · Answer 10 · 2018-12-15 18:38:55

66

Views

If $1\le a_1<\cdots<a_n\le 2n$ satisfy $\operatorname{lcm}(a_i,a_j)>2n$ for $i\ne j$, is $a_i>\frac{2n}{3}$ for all $i$?

Published on 15 Dec 2018 - 18:38

score 33 · Answer 11 · 2018-12-23 17:51:15

33

Views

Find minimum integer $n$ and $m$ such that $36^n = 16^m, n \in \mathbb{Z}, m \in \mathbb{Z}$?

Published on 23 Dec 2018 - 17:51

score 1.2k · Answer 12 · 2018-12-26 16:24:10

1.2k

Views

Relation between GCD and LCM

Published on 26 Dec 2018 - 16:24

score 911 · Answer 13 · 2018-12-28 21:51:46

911

Views

LCM and GCD polynomial relationship

Published on 28 Dec 2018 - 21:51

score 512 · Answer 14 · 2019-01-04 10:37:16

512

Views

$S_3\oplus S_3$ has an element of order $4,6,9$ or $18$.

Published on 04 Jan 2019 - 10:37

score 54 · Answer 15 · 2026-02-23 03:52:40

54

Views

Is it true that if $x \ge 2000$, then the least common multiple of $\{1,2,3,\dots,x\}$ is greater than $2.499^x$

Published on 23 Feb 2026 - 3:52

List Question

Prove $\frac{ab}{m} = \gcd(a,b)$ when $m=\operatorname{lcm}(a,b)$, for all natural numbers $a$ and $b$.

Is this approach valid for using least common multiple to establish Bertrand's postulate

Coprimality of elements of set of numbers with maximum LCM and given fixed sum.

Upper bound for a ratio of two least common multiples

Product of gcd and lcm for multivariate polynomials

If $g = gcd(a,b)$ prove (a,b)=(g). Furthermore, if $k = lcm(a,b)$ prove that $(a)\cap(b) = (k)$

Show that $\alpha = (1 2 3)(2 3 4)(5 6 7)(7 8 9 10)$ has order $10$ in $S_n$ $(n\geq10)$.

Using least common multiple to prove there exists a prime between $2x$ and $3x$

Is this proof acceptable?

If $1\le a_1<\cdots<a_n\le 2n$ satisfy $\operatorname{lcm}(a_i,a_j)>2n$ for $i\ne j$, is $a_i>\frac{2n}{3}$ for all $i$?

Find minimum integer $n$ and $m$ such that $36^n = 16^m, n \in \mathbb{Z}, m \in \mathbb{Z}$?

Relation between GCD and LCM

LCM and GCD polynomial relationship

$S_3\oplus S_3$ has an element of order $4,6,9$ or $18$.

Is it true that if $x \ge 2000$, then the least common multiple of $\{1,2,3,\dots,x\}$ is greater than $2.499^x$

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