What is the LCM of 109 and 12?

Answer 1

The answer is 1308. The trick is to notice that (12)(9)=108 which differs from 109 by only one. Now just consider the set of equivalence classes in Nmod12. the LCM of 109 and 12 will be apart of the equivalence class 0, so for every integer n between 1 and 12, (n)(109) is apart of the equivalence class n. In conclusion, the LCM must be the product (12)(109).