Math Problem Statement

Tuliskan definisi FPB dan KPK! Hitung FPB (3579, 4567) dengan Algoritma Euclid dan tuliskan langkah-langkahnya. Hitung KPK (3579, 4567) menggunakan poin b. Tulis definisi persamaan linear Diophantine dan selesaikan 24x + 14y = 2.

Solution

The uploaded image contains the following mathematical tasks:

  1. a. Write definitions for FPB (Greatest Common Divisor, GCD) and KPK (Least Common Multiple, LCM).
    b. Calculate the FPB (GCD) of 3579 and 4567 using the Euclidean Algorithm. Show the steps.
    c. Calculate the KPK (LCM) of 3579 and 4567 using the result from part b.

  2. Write the definition of a linear Diophantine equation and solve 24x+14y=224x + 14y = 2.

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Math Problem Analysis

Mathematical Concepts

Number Theory
Greatest Common Divisor (GCD)
Least Common Multiple (LCM)
Euclidean Algorithm
Linear Diophantine Equations

Formulas

Euclidean Algorithm for GCD: GCD(a, b) = GCD(b, a mod b)
LCM Formula: LCM(a, b) = |a * b| / GCD(a, b)

Theorems

Euclidean Algorithm
Basic Properties of LCM and GCD

Suitable Grade Level

Grades 8-10

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