2016 AMC 8 Problems/Problem 20
The least common multiple of and
is
, and the least common multiple of
and
is
. What is the least possible value of the least common multiple of
and
?
Solution
We wish to find possible values of ,
, and
. By finding the greatest common factor of
and
, algebraically, it's some multiple of
and from looking at the numbers, we are sure that it is 3, thus
is 3. Moving on to
and
, in order to minimize them, we wish to find the least such that the least common multiple of
and
is
,
. Similarly with
and
, we obtain
. The least common multiple of
and
is
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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