How to find the great common factor (GCF) and the least common multiple (LCM) using prime factorization?

Using prime factorization to find the GCF and the LCM is very useful, you can find the GCF and the LCM of large numbers in a small amount of time in just 4 steps.

  • The steps to find the GCF and the LCM are simple:

Step 1: Find the number’s factor.

Step 2: Write down all the factors and pair them up.

After doing this you can find the GCF and the LCM:

  • To find the GCF , there is only one step you should follow:

Step 1: Multiply the numbers that have a pair with each other, for example: if 2 and 5 have a pair you should multiply 2\cdot5 (Attention, you shoud not multiply 2\cdot2\cdot5\cdot5,  because you just have one digit per pair.).

  • To find the LCM, there is also only one step after finding the GCF:

Step 1: Multiply the GCF with all the numbers that does not have a pair.

Examples:

10 and 25

 

8204 and 504