Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2013 UNCO Math Contest II Problems/Problem 2

Revision as of 17:21, 19 October 2014 by Timneh (talk | contribs) (moved 2013 UNC Math Contest II Problems/Problem 2 to 2013 UNCO Math Contest II Problems/Problem 2: disambiguation of University of Northern Colorado with University of North Carolina)

Problem

EXAMPLE: The number $64$ is equal to $8^2$ and also equal to $4^3$, so $64$ is both a perfect square and a perfect cube.

(a) Find the smallest positive integer multiple of $12$ that is a perfect square.

(b) Find the smallest positive integer multiple of $12$ that is a perfect cube.

(c) Find the smallest positive integer multiple of $12$ that is both a perfect square and a perfect cube.

Solution

See Also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2013_UNCO_Math_Contest_II_Problems/Problem_2&oldid=65128"