Difference between revisions of "2016 AMC 8 Problems/Problem 20"
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+ | == Video Solution == | ||
+ | https://youtu.be/HISL2-N5NVg?t=2340 | ||
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+ | ~ pi_is_3.14 |
Revision as of 23:22, 27 January 2021
Problem
The least common multiple of and is , and the least common multiple of and is . What is the least possible value of the least common multiple of and ?
Solution
We wish to find possible values of ,, and . By finding the greatest common factor of and , algebraically, it's some multiple of and from looking at the numbers, we are sure that it is 3, thus is 3. Moving on to and , in order to minimize them, we wish to find the least such that the least common multiple of and is , . Similarly with and , we obtain . The least common multiple of and is
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
Video Solution
https://youtu.be/HISL2-N5NVg?t=2340
~ pi_is_3.14