The method of finding the greatest common factor and lowest common multiple that I learned in class is using prime factorization.

A different method is listing all  the factors of each number and then finding the greatest one.

For example: 125 and 250

125 = 1, 5, 25 and 125 

250 = 1, 2, 5, 10, 25, 50, 125, 250

Looking at all the factors you can see that 125 is the greatest factor that they have in common, therefore GCF of 125 and 250 = 125

A different method than prime factorization for finding the lowest common multiple is listing all the multiples of the numbers that you have and choosing the lowest one.

For example: 175 and 225

175 = 175, 350, 525, 700, 875, 1050, 1225, 1400, 1575, 1750, 1925…

225 = 225, 450, 675, 900, 1125, 1350, 1575, 1800…

Looking at the multiples of each number, you can see that 1575 is the lowest multiple that each number has in common, meaning, LCM of 175 and 225 = 1575

The method I prefer to use is the method we discussed in class, prime factorization. Using prime factorization to find the LCM and GCF is quicker in my opinion. This method takes less time to complete and requires less processing because you don’t need to list all the factors/multiples, especially because there is an infinite amount of multiples for any number.