The greatest common factor (GCF) is the largest number shared between two elements of a numerable and infinite set called integers. This means that when broken down into their lowest multiples, the largest number shared is their greatest common factor. A number which must be able to be divided by itself and one is called a Prime number. The lowest common factor (LCM), in contrast, is such that when the multiples of the two numbers are listed out individually.
The smallest number shared is regarded as their lowest common factor. This number must carry the ability to be divided by itself, one and any other multiples, and perhaps another multiple shared by the two numbers (that is composite numbers). So, in essence, the major difference between the greatest common factor GCF and the Lowest Common Factor LCM is that the earlier is concerned with what number is able to divide into two even numbers while the latter is based upon what lowest number is shared by the two numbers and can be divided by them both