Cara Menghitung KPK dan FPB

>Hello Sohib EditorOnline, in this article we will discuss about how to calculate the KPK (Least Common Multiple) and FPB (Greatest Common Factor) of two or more numbers. These two mathematical concepts are important in various fields such as engineering, computer science and even in our daily lives. So, let’s get started!

What is KPK?

KPK, or Least Common Multiple, is the smallest number that is a common multiple of two or more numbers. For example, the KPK of 4 and 6 is 12, because 12 is the smallest number that is divisible by both 4 and 6.

To calculate the KPK of two or more numbers, we need to find their prime factors and then multiply the highest exponent of each prime factor. Let’s take an example to understand this:

Number	Prime Factors	Highest Exponent
12	2 x 2 x 3	2 x 1 x 1 = 2
18	2 x 3 x 3	1 x 2 x 1 = 2
24	2 x 2 x 2 x 3	3 x 1 x 1 = 3

To find the KPK of 12, 18 and 24, we multiply the prime factors with the highest exponent:

KPK = 2³ x 3² = 72

So, the KPK of 12, 18 and 24 is 72.

What is FPB?

FPB, or Greatest Common Factor, is the largest number that is a factor of two or more numbers. For example, the FPB of 12 and 18 is 6, because 6 is the largest number that is a factor of both 12 and 18.

To calculate the FPB of two or more numbers, we need to find their prime factors and then multiply the lowest exponent of each prime factor. Let’s take an example to understand this:

Number	Prime Factors	Lowest Exponent
12	2 x 2 x 3	2 x 1 x 0 = 0
18	2 x 3 x 3	1 x 2 x 0 = 0
24	2 x 2 x 2 x 3	3 x 0 x 0 = 0

To find the FPB of 12, 18 and 24, we multiply the prime factors with the lowest exponent:

FPB = 2⁰ x 3⁰ = 1

So, the FPB of 12, 18 and 24 is 1.

How to Calculate KPK and FPB?

Step 1: Find the Prime Factors

The first step is to find the prime factors of the numbers. To do this, we can use factor trees or prime factorization method. Let’s take an example:

Find the KPK and FPB of 12, 18 and 24.

Prime factors of 12: 2 x 2 x 3

Prime factors of 18: 2 x 3 x 3

Prime factors of 24: 2 x 2 x 2 x 3

Step 2: Identify the Highest and Lowest Exponent

The second step is to identify the highest and lowest exponent for each prime factor. Let’s take an example:

Number	Prime Factors	Highest Exponent	Lowest Exponent
12	2 x 2 x 3	2 x 1 x 1 = 2	2 x 1 x 0 = 0
18	2 x 3 x 3	1 x 2 x 1 = 2	1 x 2 x 0 = 0
24	2 x 2 x 2 x 3	3 x 1 x 1 = 3	3 x 0 x 0 = 0

Step 3: Calculate the KPK and FPB

The final step is to calculate the KPK and FPB by multiplying the prime factors with the highest and lowest exponent, respectively. Let’s take an example:

KPK = 2³ x 3² = 72

FPB = 2⁰ x 3⁰ = 1

So, the KPK of 12, 18 and 24 is 72 and the FPB is 1.

FAQ

What is the use of KPK and FPB?

KPK and FPB are used in various fields such as engineering, computer science and mathematics. They are used to solve problems related to fractions, ratios, and proportions.

Can KPK be smaller than the given numbers?

No, KPK cannot be smaller than the given numbers. KPK is always a multiple of the given numbers.

Can FPB be greater than the given numbers?

No, FPB cannot be greater than the given numbers. FPB is always a factor of the given numbers.

What is the relation between KPK and LCM?

KPK and LCM are the same thing. KPK is the Indonesian term for LCM.

What is the relation between FPB and GCF?

FPB and GCF are the same thing. FPB is the Indonesian term for GCF.

What is the difference between KPK and FPB?

KPK is the least common multiple of given numbers, while FPB is the greatest common factor of given numbers.

Conclusion

In this article, we have learned how to calculate the KPK and FPB of two or more numbers. We have also discussed the important applications of these mathematical concepts in various fields. Now, you can easily calculate the KPK and FPB of any given numbers. So, keep practicing and exploring the world of mathematics!

Cara Menghitung KPK dan FPB