The method we used to find the greatest common factor and the lowest common multiple in class is by using prime factorization and finding all the prime factors.

Another method I found for finding the greatest common factor was by listing all the factors of both numbers then choosing the greatest one they have in common.
for example finding the great common factors between 135 and 185.
135= 1, 3, 5, 9, 15, 27, 45, 135…
185= 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270…
In this case the greatest common factor between the two would be 135.

Another method I found for finding the lowest common multiple was by listing all the multiples and finding the first one they have in common, making it the lowest common multiple.
For example finding the lowest common multiple between 125 and 225.
125= 125, 250, 375, 500, 625, 750, 875, 1000, 1125, 1250, 1375…
225= 225, 450, 675, 900, 1125, 1350, 1575…
In this case the lowest common multiple between the two would be 1125.

Personally I prefer the prime factorization method because it’s easier to do, much faster and less complicated.