Difference between revisions of "1987 AIME Problems/Problem 7"
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== Problem == | == Problem == | ||
| − | + | Let <math>\displaystyle [r,s]</math> denote the least common multiple of positive integers <math>\displaystyle r</math> and <math>\displaystyle s</math>. Find the number of ordered triples <math>\displaystyle (a,b,c)</math> of positive integers for which <math>\displaystyle [a,b] = 1000</math>, <math>\displaystyle [b,c] = 2000</math>, and <math>\displaystyle [c,a] = 2000</math>. | |
== Solution == | == Solution == | ||
Revision as of 00:49, 11 February 2007
Problem
Let ![$\displaystyle [r,s]$](http://latex.artofproblemsolving.com/4/2/7/427cf30ddd37bf0e036473036ff4b4cbe7684821.png)
denote the least common multiple of positive integers 
and 
. Find the number of ordered triples 
of positive integers for which ![$\displaystyle [a,b] = 1000$](http://latex.artofproblemsolving.com/e/8/7/e87aa2708304964595a5039e2797295a5fb3fc8d.png)
, ![$\displaystyle [b,c] = 2000$](http://latex.artofproblemsolving.com/7/8/5/7857365927414a9f8bb3efea5eff9a950f189437.png)
, and ![$\displaystyle [c,a] = 2000$](http://latex.artofproblemsolving.com/a/0/5/a05efcd5db4b4375e7b3cf628f7bb37e2cb1a600.png)
.
Solution
See also
| 1987 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
