The lowest common multiple (LCM) is the lowest number that is a multiple of two numbers. For example, multiples of 2 are 2, 4, 6, 8 etc, and multiples of 3 are 3, 6, 9, 12 etc, so the LCM of 2 and 3 is 6.
This is most commonly used when adding, subtracting etc fractions with different denominators.
http://www.mathsisfun.com/least-common-multiple.html
The greatest common factor (GCF) is the opposite; it is the largest number that is a factor of two whole numbers. For example, factors of 12 are 1, 2, 3, 4, 6 and 12, and factors of 15 are 1, 3, 5 and 15, so the GCF of 12 and 15 is 3.
These are most commonly used to simplify fractions.
http://www.mathsisfun.com/greatest-common-factor.html
