MS_Kekas wrote: Consider $5$ distinct positive integers. Can their mean be a)Exactly $3$ times larger than their largest common divisor? Yes, choose for example $1,2,3,10,14$ MS_Kekas wrote: b)Exactly $2$ times larger than their largest common divisor? Yes, choose for example $1,2,3,4,10$

pco wrote: MS_Kekas wrote: Consider $5$ distinct positive integers. Can their mean be a)Exactly $3$ times larger than their largest common divisor? Yes, choose for example $1,2,3,10,14$ I'm not sure, I understand. It seems to me that the largest common divisor is $1$ while the (arithmetic) mean is $6$ in this case...

Tintarn wrote: I'm not sure, I understand. It seems to me that the largest common divisor is $1$ while the (arithmetic) mean is $6$ in this case... I considered that the largest common divisor is the greatest common divisor amongst all the ten pairs $(1,2),(1,3),(1,10),(1,14),(2,3),....,(10,14)$, which is $ 2$ Maybe the OP meant $\gcd(1,2,3,10,14)$ .... .