2005 AMC 10A Problems/Problem 22
Problem
Let be the set of the
smallest positive multiples of
, and let
be the set of the
smallest positive multiples of
. How many elements are common to
and
?
Solution
Since the least common multiple , the elements that are common to
and
must be multiples of
.
Since and
, several multiples of
that are in
won't be in
, but all multiples of
that are in
will be in
. So we just need to find the number of multiples of
that are in
.
Since every
rd element of
will be a multiple of
Therefore the answer is