**How to Find KPK and FPB** – KPK and FPB are one of the materials for mathematics lessons that have been taught starting from elementary school. This material always appears in the test questions and national exams. Especially in this article, I will try to thoroughly discuss the material on how to choose the KPK and FPB as well as some patterns of questions and their discussion so that it is easier for you to understand the material that I have explained.

There are several things that must be understood before we discuss the material on the KPK and FPB. To choose KPK and GCF you must understand prime numbers and the concept of prime factorization. That’s why, here **math formula** Try to explain the definition of the two terms first. Here is the explanation:

**Material, Definition, and Method of Determining KPK and FPB**

**Prime Factor and Prime Factorization**

**prime factor** We can interpret it as the factors possessed by a number which is a prime number. Whereas **prime factorization** is the prime number product of a number. The GCF and LCM of two or three numbers can be determined by using the prime factorization.

To find the prime factors of a number, the concept of a factor tree is usually used. For example, here is the factor tree for the prime factor of 80:

From the factor tree we get the result 2 x 2 x 2 x 2 x 5 = 2^{4} x 5

So the prime factor of 80 is 2 .^{4 }x 5

**GCF (Greatest Common Factor)**

GCF or Greatest Common Factor can be interpreted as the actual circle number that has the largest value that can evenly divide two or more numbers. There are various ways that can be done to find FPB, here are some of the easiest:

#### **Practical Ways to Determine GCF:**

**With Guild Factor **

The plot factor is the number of factors that are the same from two or more numbers. GCF is taken from the factor that has the greatest value.

**Example Question 1:**

Find the GCF of 6, 9, and 18…

**Discussion:**

Factor of 6 is = {1, 2, 3, 6}

Factor of 9 is = {1, 3, 9}

The factor of 18 is = {1, 2, 3, 6, 9, 18}

The common factors of the three numbers are 1, 2, 3 .

The largest value of this factor is 3, so the GCF of 6, 9, and 18 is 3

**With Prime Factorization**

- Write these numbers in prime factor form.
- After that take the same factors of these numbers.
- If the same factor has different powers, then take the factor that has the smallest power value.

**Example Question 2:**

Find the GCF of 48, 72, and 96 …** **

**Discussion:**

First, find the factorization of the three numbers.

From the three factor trees above, we get:

48 = 2^{4} x **3**

72 = **2 ^{3}** x 3

^{2}

96 = 2^{5 }x 3

To find the GCF then use the same prime factor and also the smallest power, then the GCF of 48, 72, and 96 is 2^{3} x 3 = 8 x 3 = 24

**Least Common Multiple (KPK)**

LCM or Least Common Multiple is the actual circle number with the smallest value that can be divisible by both numbers. There are several methods you can do to find the KPK. Here’s the explanation:

**With Guild Multiples**

LCM can be taken from multiples of the plot between two or more numbers.

**Example Question 4:**

Find the LCM of 6 and 9

**Discussion:**

A multiple of 6 is = {6, 12, 18, 24, 30, 36, 42, 48, 54, …}

A multiple of 9 is = {9, 18, 27, 36, 45, 54, 63, 72, 81, …}

The same multiple of both numbers is 18, so the LCM of 6 and 9 is 18

**With Prime Factorization**

Write the numbers in prime factor form.

Take all the common factors of the numbers.

If the same factor has different powers, then take the factor with the largest exponent.

**Example Question 4:**

Find the LCM of 42, 63, and 84 …

**Discussion:**

Make a factor tree of these three numbers:

From the factor tree we get:

42 = 2 x 3 x** 7**

63 = **3 ^{2}** x 7

84 = **2 ^{2}**

^{ }x 3 x 7

To find the LCM, use prime factors that are different and have the greatest exponent.

LCM = 2^{2} x 3^{2} x 7 = 252

Then the LCM of 42, 63, and 84 is 252