2022 AMC 10A Problems/Problem 7
- The following problem is from both the 2022 AMC 10A #7 and 2022 AMC 12A #4, so both problems redirect to this page.
Contents
Problem
The least common multiple of a positive integer and is , and the greatest common divisor of and is . What is the sum of the digits of ?
Solution 1
Note that Let It follows that:
- From the least common multiple condition, we have from which and
- From the greatest common divisor condition, we have from which
Together, we conclude that The sum of its digits is
~MRENTHUSIASM ~USAMO333
Solution 2
The options for are , , and . The options for are , , , , etc. We see that appears in both lists; therefore, .
~MrThinker
Remark
If you ignore or mess up the LCM, and get , you'll still get the correct answer.
Video Solution 1
~Education, the Study of Everything
Video Solution 2
~savannahsolver
Video Solution 3 (Smart and Simple)
https://youtu.be/7yAh4MtJ8a8?si=o-aImrVOwbH1HoZv&t=673
~Math-X
Video Solution 4
See Also
2022 AMC 10A (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 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2022 AMC 12A (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 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.