Question

Prove that the least common multiple of two nonzero integers exists and is unique?

Hi Prof, this is second time Iam posting this question due unsatisfactory answer. Please show me all your steps in handwritten paper, and please be generous of all your explanation. Thanks in advance.

Answer 1

VO m and pron bilind fill came tumbling at Fol cet a bezt, a, b to Existence ut A =EKEN I alare bla3.A+01 abea as ablx) - 7 smallest element of A say. m by well ordering principle. As MEA, alm, blm. let n be euch that. aln & bln 4 mln By division algo algoutum nemqtt, ocrcm where q & r are unique Then s= n-ng. As aln re alm > alr , similarly, bli re we get r=0 mln Unipreness let n sem be eam (a,b) nm remla (aub both divide in an) => n = m. flence, done 82 ACIVE Sky