2024 AMC 10A Problems/Problem 5
- The following problem is from both the 2024 AMC 10A #5 and 2024 AMC 12A #4, so both problems redirect to this page.
Contents
[hide]- 1 Problem
- 2 Solution
- 3 Video Solution
- 4 Video Solution by Math from my desk
- 5 Video Solution (⚡️ 1 min solve ⚡️)
- 6 Video Solution by Pi Academy
- 7 Video Solution by Daily Dose of Math
- 8 Video Solution 1 by Power Solve
- 9 Video Solution by SpreadTheMathLove
- 10 Video Solution by TheBeautyofMath
- 11 See also
Problem
What is the least value of such that
is a multiple of
?
Solution
Note that in the prime factorization. Since
is a multiple of
and
we conclude that
is a multiple of
Therefore, we have
Remark
Memorizing the prime factorization of the current year is useful for the AMC 8/10/12 Exams.
~MRENTHUSIASM
Video Solution
Video Solution by Math from my desk
https://www.youtube.com/watch?v=fAitluI5SoY&t=3s
Video Solution (⚡️ 1 min solve ⚡️)
~Education, the Study of Everything
Video Solution by Pi Academy
https://youtu.be/GPoTfGAf8bc?si=JYDhLVzfHUbXa3DW
Video Solution by Daily Dose of Math
~Thesmartgreekmathdude
Video Solution 1 by Power Solve
https://youtu.be/j-37jvqzhrg?si=qwyiAvKLbySyDR7D&t=529
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=6SQ74nt3ynw
Video Solution by TheBeautyofMath
For AMC 10: https://youtu.be/uKXSZyrIOeU?t=1168
For AMC 12: https://youtu.be/zaswZfIEibA?t=984
~IceMatrix
See also
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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 |
2024 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.