Cara Menentukan FPB dan KPK

>Hello Sohib EditorOnline, if you’re reading this article, chances are you’re struggling with finding the FPB and KPK of two or more numbers. Don’t worry, these mathematical concepts may seem daunting at first, but with proper guidance, you’ll master them in no time.

Apa itu FPB dan KPK?

FPB stands for Faktor Persekutuan Besar or Greatest Common Factor (GCF) in English. It’s the largest factor that divides two or more numbers. KPK, on the other hand, stands for Kelipatan Persekutuan Kecil or Least Common Multiple (LCM) in English. It’s the smallest multiple that two or more numbers have in common.

Perbedaan antara FPB dan KPK

Although FPB and KPK are closely related, they have distinct differences. FPB is used to find the largest factor between two or more numbers, while KPK is used to find the smallest multiple shared between them.

For instance, if you have two numbers 12 and 20, their FPB is 4 because 4 is the largest factor that both numbers share. Their KPK, on the other hand, is 60 because 60 is the smallest multiple that they have in common.

Cara Menentukan FPB dengan Faktorisasi Prima

There are several methods to determine FPB, but one of the most common is through prime factorization. Here’s how:

Step 1: Factorize the Numbers

Let’s say you want to find the FPB of 24 and 36. You need to factorize both numbers into prime factors.

24 36
2 x 2 x 2 x 3 2 x 2 x 3 x 3

As you can see, 24 can be expressed as 2 x 2 x 2 x 3, while 36 is 2 x 2 x 3 x 3.

Step 2: Identify Common Prime Factors

Next, you need to identify the common prime factors between the two numbers.

24 36
2 x 2 x 2 x 3 2 x 2 x 3 x 3

The common prime factors are 2, 2, and 3.

Step 3: Multiply the Common Prime Factors

Finally, you need to multiply the common prime factors to get the FPB.

24 36
2 x 2 x 2 x 3 2 x 2 x 3 x 3
2 x 2 x 3 = 12

The FPB of 24 and 36 is 12.

Cara Menentukan KPK dengan FPB

If you already know the FPB of two or more numbers, you can use it to find their KPK. Here’s how:

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Step 1: Multiply the Numbers

Let’s say you want to find the KPK of 4, 6, and 8. The first step is to multiply the numbers.

4 x 6 x 8 = 192

Step 2: Divide by the FPB

Next, you need to divide the product by the FPB of the numbers.

FPB(4, 6, 8) = 2

192 ÷ 2 = 96

Step 3: Simplify

The result is the KPK of the numbers. In this case, it’s 96. However, you can simplify the number to its prime factors (if necessary).

96 = 2 x 2 x 2 x 2 x 2 x 3

The KPK of 4, 6, and 8 is 96.

Kapan FPB dan KPK Digunakan?

FPB dan KPK sering digunakan dalam matematika, terutama dalam operasi pecahan. FPB digunakan untuk menyederhanakan pecahan, sedangkan KPK digunakan untuk menemukan denominasi yang sama pada pecahan.

Contoh Penerapan FPB dan KPK pada Pecahan

Let’s say you want to add ⅖ and ⅓. You need to find the denominators that are the same for both fractions. Here’s how:

Step 1: Find the KPK of 5 and 3

KPK(5, 3) = 15

Step 2: Convert the Fractions to Have the Same Denominator

Convert ⅖ and ⅓ so that they have the same denominator (15).

⅖ = 6/15

⅓ = 5/15

Step 3: Add the Fractions

6/15 + 5/15 = 11/15

The result is 11/15.

FAQ

1. Apa Perbedaan Antara FPB dan KPK?

FPB digunakan untuk menemukan faktor terbesar yang dibagi oleh dua atau lebih bilangan, sedangkan KPK digunakan untuk menemukan kelipatan terkecil yang dimiliki oleh dua atau lebih bilangan.

2. Bagaimana Cara Menentukan FPB?

Ada beberapa cara untuk menentukan FPB, salah satunya dengan faktorisasi prima. Anda harus memfaktorkan bilangan menjadi faktor prima, mengidentifikasi faktor prima yang sama, dan mengalikan faktor-faktor primer tersebut.

3. Bagaimana Cara Menentukan KPK?

Anda dapat menentukan KPK dengan menggunakan FPB. Pertama, kalikan bilangan-bilangan tersebut. Kemudian, bagi hasil kalinya dengan FPB bilangan-bilangan tersebut. Hasilnya adalah KPK.

4. Kapan FPB dan KPK Digunakan?

FPB dan KPK sering digunakan dalam operasi pecahan, persamaan, trigonometri, dan banyak lagi. Mereka merupakan konsep dasar dalam matematika.

5. Apa Saja Metode yang Dapat Digunakan untuk Menentukan FPB?

Selain faktorisasi prima, metode lain yang dapat digunakan untuk menentukan FPB adalah algoritma Euclidean, sistem faktor ekspansi, dan faktorisasi kuadratik.

Cara Menentukan FPB dan KPK