Difference between revisions of "2016 AMC 8 Problems/Problem 20"
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We wish to find possible values of <math>a</math>, <math>b</math>, and <math>c</math>. By finding the greatest common factor of <math>12</math> and <math>15</math>, we can find that <math>b</math> is 3. Moving on to <math>a</math> and <math>c</math>, in order to minimize them, we wish to find the least such that the least common multiple of <math>a</math> and <math>3</math> is <math>12</math>, <math>\rightarrow 4</math>. Similarly, with <math>3</math> and <math>c</math>, we obtain <math>5</math>. The least common multiple of <math>4</math> and <math>5</math> is <math>20 \rightarrow \boxed{\textbf{(A)} 20}</math> | We wish to find possible values of <math>a</math>, <math>b</math>, and <math>c</math>. By finding the greatest common factor of <math>12</math> and <math>15</math>, we can find that <math>b</math> is 3. Moving on to <math>a</math> and <math>c</math>, in order to minimize them, we wish to find the least such that the least common multiple of <math>a</math> and <math>3</math> is <math>12</math>, <math>\rightarrow 4</math>. Similarly, with <math>3</math> and <math>c</math>, we obtain <math>5</math>. The least common multiple of <math>4</math> and <math>5</math> is <math>20 \rightarrow \boxed{\textbf{(A)} 20}</math> | ||
− | == Video Solution == | + | == Video Solution by OmegaLearn== |
https://youtu.be/HISL2-N5NVg?t=2340 | https://youtu.be/HISL2-N5NVg?t=2340 | ||
~ pi_is_3.14 | ~ pi_is_3.14 | ||
+ | == Video Solution == | ||
https://youtu.be/7tGFq07njVo | https://youtu.be/7tGFq07njVo | ||
Revision as of 04:07, 16 January 2023
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
, we can find that
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
Video Solution by OmegaLearn
https://youtu.be/HISL2-N5NVg?t=2340
~ pi_is_3.14
Video Solution
~savannahsolver
See Also
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.