ABSTRACT ALGEBRA PROOFPlease provide a super detail proof for part (a). Please be detail and clear each step of the proof. Only solve if you fully understand. Do not provide an incomplete proof. Thanks.
11.) LCM and GCD. The least common multiple of nonzero integers a and b is the smallest positive integer m such that a | m and b |m; m is usually denoted (a, b]. Prove that (a) Whenever a | k and b | k, then [a, b] | k; (btria, b]- ab/(a, b) if a 0 and b >0. qcd(a, b)
Show transcribed image text11.) LCM and GCD. The least common multiple of nonzero integers a and b is the smallest positive integer m such that a | m and b |m; m is usually denoted (a, b]. Prove that (a) Whenever a | k and b | k, then [a, b] | k; (btria, b]- ab/(a, b) if a 0 and b >0. qcd(a, b)