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How to show that $\displaystyle [a,b,c] = \frac{abc}{(ab,bc,ca)}$ without prime factorization?
elementary-number-theory
least-common-multiple
gcd-and-lcm
Can the identity $ab=\gcd(a,b)\text{lcm}(a,b)$ be recovered from this category?
elementary-number-theory
category-theory
divisibility
gcd-and-lcm
least-common-multiple
Proving that $a \mathbb{Z} \cap b\mathbb{Z} = \operatorname{lcm}(a,b)\mathbb Z$ [duplicate]
abstract-algebra
elementary-number-theory
least-common-multiple
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
group-theory
finite-groups
abelian-groups
least-common-multiple
why $ \rm{lcm}[1,2,3,\cdots,n]\in (2^n,4^n)$
number-theory
inequality
prime-numbers
approximation
least-common-multiple
The series of reciprocals of the least common multiples of integers $X_1<X_2<\dots$ converges
real-analysis
sequences-and-series
number-theory
least-common-multiple
Reason for LCM of all numbers from 1 .. n equals roughly $e^n$
number-theory
exponential-function
least-common-multiple
Is $\mbox{lcm}(a,b,c)=\mbox{lcm}(\mbox{lcm}(a,b),c)$?
elementary-number-theory
discrete-mathematics
divisibility
least-common-multiple
Proving that any common multiple of two numbers is a multiple of their least common multiple
elementary-number-theory
divisibility
least-common-multiple
Prove the LCM (Least Common Multiple).
elementary-number-theory
discrete-mathematics
gcd-and-lcm
least-common-multiple
Find the least number which when divided by 2, 3, 4, 5, 6 leaves a remainder of 1 but it is divided by 7 completely.
puzzle
least-common-multiple
If $m=\operatorname{lcm}(a,b)$ then $\gcd(\frac{m}{a},\frac{m}{b})=1$
number-theory
elementary-number-theory
gcd-and-lcm
least-common-multiple
Show that $\rm lcm(a,b)=ab \iff gcd(a,b)=1$
elementary-number-theory
divisibility
gcd-and-lcm
least-common-multiple
$\text{lcm}(1,2,3,\ldots,n)\geq 2^n$ for $n\geq 7$
number-theory
inequality
prime-numbers
least-common-multiple
Beginner: How to complete the induction case in a proof that all multiples are a product of the least common multiple
elementary-number-theory
proof-writing
arithmetic
least-common-multiple
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
elementary-number-theory
divisibility
gcd-and-lcm
least-common-multiple
Concise proof that every common divisor divides GCD without Bezout's identity?
number-theory
elementary-number-theory
divisibility
gcd-and-lcm
least-common-multiple
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
elementary-number-theory
divisibility
gcd-and-lcm
least-common-multiple
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
number-theory
divisibility
gcd-and-lcm
least-common-multiple
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