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1987 AIME Problems
7
7
Part of
1987 AIME Problems
Problems
(1)
LCM triples
Source:
3/16/2006
Let
[
r
,
s
]
[r,s]
[
r
,
s
]
denote the least common multiple of positive integers
r
r
r
and
s
s
s
. Find the number of ordered triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of positive integers for which
[
a
,
b
]
=
1000
[a,b] = 1000
[
a
,
b
]
=
1000
,
[
b
,
c
]
=
2000
[b,c] = 2000
[
b
,
c
]
=
2000
, and
[
c
,
a
]
=
2000
[c,a] = 2000
[
c
,
a
]
=
2000
number theory
least common multiple
symmetry
AMC
AIME