1978 AHSME Problems/Problem 27
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Solution
Let this integer be . We have
,
,
.
Recall that if
and
then
We see that since
,
,
.
We have
From to
,
contains the largest power of
,
contains the largest power of
, and
contains the largest power of
. Thus, our lcm is equal to
Since
, our
smallest values of
are
and
The difference between these values is simply the value of
~JustinLee2017