Thread: if (a,b)=1 and (b,c)=1, then (a,c)=1

1. if (a,b)=1 and (b,c)=1, then (a,c)=1

if $(a,b)=1$ and $(b,c)=1$, then $(a,c)=1$

So $1|a, \ 1|b, \ 1|c$

How can I show $1=gcd(a,c)$??

2. Re: if (a,b)=1 and (b,c)=1, then (a,c)=1

Originally Posted by dwsmith
if $(a,b)=1$ and $(b,c)=1$, then $(a,c)=1$
So $1|a, \ 1|b, \ 1|c$
How can I show $1=gcd(a,c)$??
Consider $(9,8)=1,~(8,3)=1~\&~(9,3)=3~.$
Is is the it true?