GCF and LCM

This week when looking through the book and starting my homework, I was at the same daze I always am when it comes to finding the greatest common factor and least common multiple. I always seem to get the two confused with each other! After reading through the book more and doing some of the examples I definitely understand the information a lot better. A few of the things that helped me (and that can hopefully help you) were to have the definitions in front of me, examples to look back at, and the steps to refer to.

Greatest Common Factor - the greatest natural number that is a factor of both numbers. (Also known as the greatest common divisor, GCD)

Example: Finding the GCF of 24 and 30.
                 A= the set of factors of 24= {1,2,3,4,6,8,12,24}
                 B= the set of factors of 30= {1,2,3,5,6,10,15,30}
                 The set of common factors of 24 and 30 = {1,2,3,6}
                 ANSWER: 6 is the GCF of 24 and 30.

Least Common Multiple - the smallest natural number that is a multiple of both the natural numbers.

Example: Finding the LCM of 6 and 8.
                C= the set of multiples of 6= {0,6,12,24,30,36,42,48....}
                D= the set of multiples of 8= {0,8,16,24,32,40,48,56,64....}
                The set of multiples of 6 and 8 = {0,24,48..}
                ANSWER: 24 is the LCM of 6 and 8.

I found a great website that gives you step by step instructions on finding the GCF and LCM. It gives great examples and understanding. I hope this website is as useful to you as it was to me!

http://www.purplemath.com/modules/lcm_gcf.htm

After going through these definitions and examples finding the GCF and LCM was like riding a bike... I will remember how to do it now and years down the road. I hope this information helps you as much as it helped me!