In this post, I’m supposed to find another method of finding the **Greatest Common Factor** (**GCF**) and** Least Common Multiple** (**LCM**) other than the prime factorization.

This method goes the same for *both GCF and LCM*.

E.g. Find the GCF and LCM of **180** and **360**.

Step 1. Find **a single number** that can be **divided by both of them or is divisible by both numbers**.

180 and 360 can be divided by 10, 9, 2… but in this case, we will use 10 since it’ll get easier since it is a large number.

Step 2. **Divide the base numbers by the number you chose.**

180/10 = 18

360/10 = 36

Step 3. **Repeat step one and step two**, and this time, *using the quotient of the two base numbers*, **until you reach the point where the quotients can’t be divided by a number anymore**.

18/9 = 2 | 36/9=4

2/2 = 1 | 4/2 = 2

Step 4.

**For finding GCF**: Now, to find the GCF,**get all the numbers you chose to divide the base numbers and the quotients by**. After that,**multiply all of them altogether**and the product of those numbers is the GCF.- The numbers I picked were 10, 9, and 2. So:
- 10 * 9 * 2 = 180.
- The GCF of 180 and 360 is 180.

**For finding LCM**: Now, to find the LCM,**get all the numbers you chose to divide the base numbers and the quotients by, also get the LAST quotients of your two numbers**. After that,**multiply all of them altogether**and the product of those numbers is the LCM.- The numbers I picked were 10, 9, 2 and the last quotients of the two numbers were 1 and 2, so:
- 10 * 9 * 2 * 1 * 2 = 360.
- Th LCM of 180 and 360 is 360.

Solution: Find the GCF and LCM of 180 and 360

If you have to ask me, I really prefer the method I learned in class, which is ** prime factorization **because it’s much easier to me and it doesn’t really do much work than this method I presented.