I have the following :

1. a_{1} | a
2. b_{1} | b
3. a_{1}b_{1} | ab
4. a_{1}b_{1} | k
5. a | k
6. k | ab
7. k | aa_{1}b_{1}

I need to show that k=ab_{1}.
I try to show that k | ab_{1} and ab_{1} | k, but I dont know how to show this.