Question:
My name is Nahiyan. I would like to know what is the LCM of (-1) and (+1) is. Here I am writting down some of my thaughts on this.
If 1 is factorized, we get
1 = 1
= (-1)*(-1)
= (-1)*(-1)*(+1)
= ...
= (-1)*(-1)*(-1)*(-1)........ [and so on...]
If (-1) is factorized, we get
-1 = -1
= (-1)*(+1)
= (-1)*(-1)*(-1)
= ...
= (-1)*(-1)*(-1)*(-1)*(-1)...... [and so on...]
So, to get the LCM, we are supposed to take infinite numbers of (-1). What will be the sign then? Will the final result be positive or negetive ?
This is the point where I am getting confused. Would you please help me ? Thank you for your time.
Hi Nahiyan
We would normally define the least common multiple as the smallest positive integer that is a multiple of those under consideration, thus the lcm{1,-1} is 1.
By the way when we factor an integer we typically mean breaking it down into its prime factors so that your 'factorisation' of 1 is not quite the right thing.
Penny