FPB dan KPK - Matematika Kelas 7 Kurikulum Merdeka

Introduction

This tutorial will guide you through understanding and calculating the highest common factor (FPB) and the least common multiple (KPK) of several numbers, based on the teachings from the video "FPB dan KPK - Matematika Kelas 7 Kurikulum Merdeka." These concepts are essential in mathematics, particularly in solving problems involving integers. By the end of this guide, you will be equipped to determine FPB and KPK confidently and apply these skills in real-world scenarios.

Step 1: Understand the Concepts of FPB and KPK

• FPB (Highest Common Factor): The largest number that divides two or more numbers without leaving a remainder.
• KPK (Least Common Multiple): The smallest number that is a multiple of two or more numbers.

Practical Tips

• To find FPB, consider the factors of each number and identify the largest one they share.
• For KPK, list the multiples of each number and find the smallest common one.

Step 2: Determine the FPB of Several Numbers

1. List the Numbers: Start with the numbers for which you want to find the FPB.
2. Find Prime Factors: Break each number down into its prime factors.
   • Example:
     • 12 = 2 × 2 × 3
     • 18 = 2 × 3 × 3
3. Identify Common Factors: Look for the prime factors that appear in each list.
4. Multiply Common Factors: Multiply the lowest powers of the common prime factors to find the FPB.
   • Example:
     • Common factors for 12 and 18: 2 and 3
     • FPB = 2^1 × 3^1 = 6

Common Pitfalls

• Forgetting to include all prime factors.
• Using higher powers of common factors instead of the lowest.

Step 3: Calculate the KPK of Several Numbers

1. List the Numbers: Write down the numbers for which you want to find the KPK.
2. Find Prime Factors: Decompose each number into its prime factors.
3. Identify All Factors: Take note of all prime factors, using the highest power of each factor.
4. Multiply the Highest Powers Together: This gives you the KPK.
   • Example:
     • For 12 and 18, the prime factors are:
       • 12 = 2^2 × 3^1
       • 18 = 2^1 × 3^2
     • KPK = 2^2 × 3^2 = 36

Step 4: Solve Word Problems Involving FPB and KPK

1. Read the Problem Carefully: Identify the numbers involved and what is being asked (FPB or KPK).
2. Extract Key Information: Note any relationships described in the problem, such as groups or sets.
3. Apply FPB or KPK Methods: Use the steps from above to find the required factor or multiple.
4. Double-Check Your Work: Ensure your calculations are accurate and reflect the problem's requirements.

Real-World Applications

• FPB is useful in simplifying fractions and finding common denominators.
• KPK is applied in problems involving scheduling events that repeat at different intervals.

Conclusion

By mastering the concepts of FPB and KPK, you are now equipped to tackle mathematical problems involving integers effectively. Practicing these steps will enhance your understanding and confidence in mathematics. For further practice, consider attempting more complex problems or engaging with additional resources on number theory.