Q: Prove if a|k, b|k, then lcm(a,b)|k.
(Hint: LCM of non-zero intergers a and b is the smallest postive integer m such that a|m, b|m)
Here are the all the details if you need them.Originally Posted by Neils Henrik Abel
Let then that means:
Now, by the above statements,
Definition: Let . For we define so that .
Theorem: Let and . Then .
Proof: Again, just follow the definitions.
Substitute second equation into first,
Since we have,