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Kvant 2024
M2779
M2779
Part of
Kvant 2024
Problems
(1)
A nice lcm problem
Source: Kvant Magazine No. 1 2024 M2779
4/7/2024
Prove that for any natural number
k
k{}
k
there is a natural number
n
n{}
n
such that
l
c
m
(
1
,
2
,
…
,
n
)
=
l
c
m
(
1
,
2
,
…
,
n
+
k
)
.
\mathrm{lcm}(1,2,\ldots,n)=\mathrm{lcm}(1,2,\ldots,n+k).
lcm
(
1
,
2
,
…
,
n
)
=
lcm
(
1
,
2
,
…
,
n
+
k
)
.
From the folklore
number theory
Lowest common multiple