2013 UNCO Math Contest II Problems/Problem 2
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.
Solution
We can factor 12 into 2*2*3. There are already two factors of two, so we only need to multiply it by 3 to get two factors of three, giving us 36.
See Also
| 2013 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
