Difference between revisions of "2007 AIME I Problems/Problem 4"
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Revision as of 20:25, 15 March 2007
Problem
Three planets orbit a star circularly in the same plane. Each moves in the same direction and moves at constant speed. Their periods are 
,
, and 
. The three planets and the star are currently collinear. What is the fewest number of years from now that they will all be collinear again?
Solution
First, take the prime factorization of all the numbers: 
, 
, and 
. To find out when they are next collinear, you take 
, which is 
See also
| 2007 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
