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Q: Is there no smallest element in the set of integers?

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Given a set of integers, the LCM is the smallest integer which is a multiple of each of element of the set.

No.

That is not true.

An element of that set.

The smallest factor of any set of positive integers is 1.

That's the smallest infinite number; it corresponds to the size of the set of integers.

It is true.

The smallest common factor of any set of positive integers is 1.

No. One of the group axioms is that each element must have an inverse element. This is not the case with integers. In other words, you can't solve an equation like: 5 times "n" = 1 in the set of integers.

The smallest common factor of any set of positive integers is 1.

The smallest is -1

The least common factor of any set of integers is 1.

The set of integers is divided into three subsets. One is the positive integers. Another is the negative integers. The last subset has one element -- zero. In sum, integers are composed of the positive integers, the negative integers, and zero.

A set of which all the elements are contained in another set. The set of even numbers is a subset of the set of integers.

The set of integers represents the integers.

The least common factor of any set of integers is 1.

The least common factor of any set of integers is 1.

The set of integers is an infinite set as there are an infinite number of integers.

The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder. The least common factor of any set of integers is 1.

The smallest positive integer is 1.

Integers

The set of positive integers contains 1 but not zero. Within the set of integers, there is the subset of positive integers, the subset of negative integers and the subset with a single element in it - zero. There are a zillion other sets that could be specified that meet the conditions set down in the question. The one cited is an easy one.

1 is the smallest positive integer. But if you include negative integers, there is no smallest.

The LCM for a set of numbers is the smallest positive integer such that each element in the set divides it evenly.

The smallest part of an element that has the properties of that element is the atom.