Difference between revisions of "2013 UNCO Math Contest II Problems/Problem 2"
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EXAMPLE: The number <math>64</math> is equal to <math>8^2</math> and also equal to <math>4^3</math>, so <math>64</math> is both a perfect square and a perfect cube. | EXAMPLE: The number <math>64</math> is equal to <math>8^2</math> and also equal to <math>4^3</math>, so <math>64</math> is both a perfect square and a perfect cube. | ||
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(a) Find the smallest positive integer multiple of <math>12</math> that is a perfect square. | (a) Find the smallest positive integer multiple of <math>12</math> that is a perfect square. | ||
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(b) Find the smallest positive integer multiple of <math>12</math> that is a perfect cube. | (b) Find the smallest positive integer multiple of <math>12</math> that is a perfect cube. | ||
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(c) Find the smallest positive integer multiple of <math>12</math> that is both a perfect square and a perfect cube. | (c) Find the smallest positive integer multiple of <math>12</math> that is both a perfect square and a perfect cube. | ||
Revision as of 15:08, 16 October 2014
Problem
EXAMPLE: The number 
is equal to 
and also equal to 
, so is both a perfect square and a perfect cube.
(a) Find the smallest positive integer multiple of 
that is a perfect square.
(b) Find the smallest positive integer multiple of that is a perfect cube.
(c) Find the smallest positive integer multiple of that is both a perfect square and a perfect cube.
