What's the empty LCM?

3 Answers

Since the order "L" refers to is the divisibility order of integers, and that the LCM is always nonnegative, then we are looking for a nonnegative number that is a multiple of every number in the empty set (any nonnegative number is valid), and that also divides every other number fulfilling the previous condition(to be the smallest division-wise).
So the lcm of the empty set has to be the nonnegative integer that divides every other nonnegative integer: that's 1
> I'm asking this because me and a lot of people need to know the standard definition of lcm(empty_list)

I would like to know who those "a lot of people" are, and why are they looking for something silly as that.

In general, we do not define lowest common multiple of an empty list. What would be the point? I guess if you want to define it using the structural recursion over the list. In that case, you are perfectly ok to set lcm(empty_list) to be whatever you want. You will not actually need it when using the function anyway.

Setting lcm(empty_list) to 1 would allow you to have a neater recursive definition, so I guess you can go with that.
Does your question arise from an application? If so, what would it need to be when the empty case occurs?