Find the Greatest Common Factor (GCF) or the Least Common Multiples (LCM) can be very intimidating and confusing. However there are tricks that can making find these things simpler.

The Greatest Common Factor can be defined as, the highest common factor between two numbers. In order to find this we need to know what all the parts are. A factor is two numbers that you can multiply together to get another number.

The Factors of 12: 1, 2, 3, 4, 6, and 12

The Factors of 30: 1, 2, 3, 5, 6, 10, 12, and 30

So we can conclude that the Greatest Common Factor is 6.

We can find the Greatest common factors by looking at factors of a number or we can find it by looking that the prime factorization. We can do this be breaking down numbers into primes.

For example:

The Prime Factors of 12 are 2 x 2 x 3

The Prime Factors of 30 are 2 x 3 x 5

12= 2 x 2 x 3

30= 2 x 3 x 5

We can find the GCF and the LCM by looking that these numbers. To find the GCF we can look at the intersection of the Prime factorization of 12 and 30. The intersection of 12 and 30 is 2 and 3; therefore the GCF is 2 x 3= 6. We can also find the LCM by looking at these numbers, to find the LCM we look at all the number of the prime factorization (the union of the numbers). The LCM of 12 and 30 is 2^2, 3 and 5; therefor the LCM is 2 x 2 x 3 x 5 =60.