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GCF/LCM

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.