1998 AIME Problems/Problem 1
Problem
For how many values of is
the least common multiple of the positive integers
and
?
Solution
It is evident that has only 2s and 3s in its prime factorization, or
.
The lcm of any numbers an be found by writing out their factorizations and taking the greatest power for each factor. The . Therefore
, and
. Since
, there are
values of
.
See also
1986 AIME (Problems • Answer Key • Resources) | ||
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Followed by Problem 2 | |
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