If a, b, and c are positive integers such that gcd(a,b) = 168 and gcd(a,c) = 490, then what is the smallest possible value of gcd(b,c)?
a ==5,880, b==6,048, c==6,370
GCD(a, b) ==GCD(5,880, 6,048) ==168
GCD(a, c) ==GCD(5,880, 6,370) ==490
GCD(b, c) ==GCD(6,048, 6,370) ==14
b divides 168 and c divides 490 by definition of gcd.
\(\gcd(b, c) \geq \gcd(168, 490) = 14\)
Therefore the smallest value is 14.
