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Why is HCF of $x^2-1$ and $x-1$ is $x-1$, "why can't it be $1-x$?"

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#least-common-multiple
470
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Let $m$ be the largest integer $\le n$ which is a power of 2.Put $l_n=LCM(1,2,3...n).$Show that $l_n/m$ is odd

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#elementary-number-theory #least-common-multiple
143
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How many shared numbers between all factors of 465 and all multiples of 3 between 20 and 100?

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#combinatorics #prime-numbers #combinations #prime-factorization #least-common-multiple
87
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Properties about gcd and lcm

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#elementary-number-theory #arithmetic #gcd-and-lcm #least-common-multiple
705
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g.c.d. and l.c.m. in $\mathbb{Z}[\sqrt{-3}]$

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#ring-theory #commutative-algebra #field-theory #gcd-and-lcm #least-common-multiple
71
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$\operatorname{lcm} (a,b)$ of rectangle's side lengths

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#algebra-precalculus #rectangles #least-common-multiple
495
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Minimizing sum of variables

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#algebra-precalculus #least-common-multiple
187
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Convergence of $\sum_{k=1}^\infty\frac{\operatorname{rad}(k!)}{\operatorname{lcm}(1,2,\ldots,k)}$

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#real-analysis #convergence-divergence #analytic-number-theory #prime-factorization #least-common-multiple
55
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Convergence of a double sum of reciprocals of lowest common multiples

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#convergence-divergence #summation #least-common-multiple
367
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$\operatorname{lcm}(a,b)=ab$ if and only if $\gcd(a,b)=1$

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#abstract-algebra #gcd-and-lcm #least-common-multiple
4.1k
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If $\gcd(a,b)=1$, then $\operatorname{lcm}(a,b)=ab$

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#elementary-number-theory #proof-verification #gcd-and-lcm #least-common-multiple
59
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how to compute $\gcd(\frac{a}{b},\frac{c}{d})$?

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#number-theory #gcd-and-lcm #least-common-multiple
50
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equality of LCM

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#elementary-number-theory #least-common-multiple
550
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Minimize $LCM(a,b,c,d)$ given $a+b+c+d=1000$

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#elementary-number-theory #least-common-multiple
356
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Minimize $a+b+c+d$ given $\text{LCM}(a,b,c,d)=1000$

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#elementary-number-theory #least-common-multiple

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