Thank you for the opportunity to help you with your question!
here gcd represents greatest common divisor.
gcd(a,b)=k, means a/k=0 and b/k = 0
gcd(b,c)=k, so b/k= 0 and c/k =0 so we get that a/k=0 and c/k=0 thus k is the greatest common divisor to a and c. thus, gcd(a,c)>=k. Please let me know if you need any clarification for the doubts. I'm always happy to answer your questions. Looking forward to help you again. thank you. :)