Difference between revisions of "2016 AMC 12B Problems/Problem 24"
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=Problem= | =Problem= | ||
| − | There are exactly <math>77,000</math> ordered quadruplets <math>(a, b, c, d)</math> such that <math>GCD(a, b, c, d) = 77</math> and <math> | + | There are exactly <math>77,000</math> ordered quadruplets <math>(a, b, c, d)</math> such that <math>GCD(a, b, c, d) = 77</math> and <math>LCM(a, b, c, d) = n</math>. What is the smallest possible value for <math>n</math>? |
<math>\textbf{(A)}\ 13,860\qquad\textbf{(B)}\ 20,790\qquad\textbf{(C)}\ 21,560 \qquad\textbf{(D)} 27,720 \qquad\textbf{(E)}\ 41,580</math> | <math>\textbf{(A)}\ 13,860\qquad\textbf{(B)}\ 20,790\qquad\textbf{(C)}\ 21,560 \qquad\textbf{(D)} 27,720 \qquad\textbf{(E)}\ 41,580</math> | ||
=Solution= | =Solution= | ||
Revision as of 13:46, 21 February 2016
Problem
There are exactly 
ordered quadruplets 
such that 
and 
. What is the smallest possible value for 
?
