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why $ \rm{lcm}[1,2,3,\cdots,n]\in (2^n,4^n)$

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#number-theory #inequality #prime-numbers #approximation #least-common-multiple
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LCM of $n$ consecutive natural numbers

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#divisibility #least-common-multiple
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If a divisor of $pq-1$ divides the LCM of $p-1$ and $q-1$, then it also divides the GCD of these two numbers

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#elementary-number-theory #divisibility #gcd-and-lcm #least-common-multiple
59
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highest power of of prime number $p$ among $k$ consecutive positive integers

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#prime-numbers #prime-factorization #least-common-multiple
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How can LCM(1/x, 1/y) be calculated?

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#least-common-multiple
8.1k
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greates number of baskets to put equal number of fruits

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#gcd-and-lcm #least-common-multiple
231
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Define $lcm(a, b) :={(ab)}/ {(gcd(a, b))}$ .Prove that $lcm(a, b)$ is the smallest positive integer that is evenly divisible by both $a$ and $b$.

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#elementary-number-theory #least-common-multiple
733
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Proving that $a \mathbb{Z} \cap b\mathbb{Z} = \operatorname{lcm}(a,b)\mathbb Z$

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#abstract-algebra #elementary-number-theory #least-common-multiple
490
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How do you prove something is the LCM of two numbers?

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#elementary-number-theory #least-common-multiple
856
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Does the LCM of $ax$ and $bx$ equal $\operatorname{lcm}(a,b)\cdot x$?

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#elementary-number-theory #divisibility #least-common-multiple
280
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Prove if If $m \in Z^+$, $a|m$, and $b|m$, then $\mbox{lcm}(a,b) \leq m$.

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#elementary-number-theory #least-common-multiple
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Is $aZ \cup b Z = \gcd(a, b)Z$?

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#abstract-algebra #gcd-and-lcm #least-common-multiple
290
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Find the sum of all the multiples of 3 or 5 below 3209.

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#summation #least-common-multiple
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How many pairs of numbers exist,which satisfy the following conditions?

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#elementary-number-theory #gcd-and-lcm #least-common-multiple
1k
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The series of reciprocals of the least common multiples of integers $X_1<X_2<\dots$ converges

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#real-analysis #sequences-and-series #number-theory #least-common-multiple

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