What is greater the GCF of 4 and 8 or the LCM?

Answer 1

Given a set of number, the GCF is a factor of every one of them. As a factor, it cannot be larger than them so the GCF is at most as large as the smallest of the number in the set.

The LCM of the same set is a multiple of each element in the set. The LCM must, therefore, be at least as great as the largest element in the set.

Thus if x is the smallest member of a set S and y is the largest, then

GCF <= x <= y <= LCM.

It can be proven that GCF = LCM if all the elements in the set are the same.

Answer 2

Most often the LCM is greater. In special cases it can be the same. It will never be less.

Answer 3

The LCM of any set of integers will never be smaller than the GCF.

Answer 4

A common factor can't be greater than the smaller number. A common multiple can't be smaller than the larger number. Factors go into numbers, numbers go into multiples.

Answer 5

The LCM will never be less than the GCF.