Q: Prove that if a and b are positive integers satisfying (a,b)=[a,b}, then a=b.
My approach (with ans): (a,b) means gcd, and I let g=(a,b) since g is the gcd, then I get these two: g|a and g|b, while g
Next is [a,b], the lcm of a and b, and I let it be h. then I get another two of these: a|h and b|h while a
Combine the inequalities together will get: g
Since the question provides that g=h, so h
Is the a correct explanation? As I hope to get full credits, I hope I can present my answers as detail as possible (without any faults). Thank you.