Question

Ребят помогите!!! Дам много баллов! Нужно лёгенькую задачку на НОК И НОД и 1-3 примера тоже НОК И НОД --------------------------- И если не трудно,можете объяснить что значит взаимно простые числа как находить общее кратное?

Answer 1

Взаимно простые это те числа у которых нет общих делителей . Например:18 и 25

Answer 2

Introduction

Sure, I can help you with that! Let's start by understanding what the terms "GCD" (Greatest Common Divisor), "LCM" (Least Common Multiple), and "mutually prime numbers" mean. Then I'll provide you with a simple problem involving GCD and LCM, as well as a few examples.

GCD and LCM

- GCD (Greatest Common Divisor): The GCD of two or more numbers is the largest number that divides each of them without leaving a remainder. - LCM (Least Common Multiple): The LCM of two or more numbers is the smallest number that is divisible by each of them without leaving a remainder. - Mutually Prime Numbers: Two numbers are said to be mutually prime (or coprime) if their GCD is 1. In other words, there are no common factors other than 1 between the two numbers.

Finding the GCD and LCM

To find the GCD and LCM of two or more numbers, you can use the following methods:

- GCD: There are several methods to find the GCD, including the Euclidean algorithm and prime factorization method. The Euclidean algorithm is commonly used and involves repeatedly dividing the larger number by the smaller number until the remainder is 0. The last non-zero remainder is the GCD of the two numbers. - LCM: To find the LCM, you can use the formula LCM(a, b) = (a * b) / GCD(a, b), where a and b are the two numbers for which you want to find the LCM.

Example Problem

Let's solve a simple problem involving GCD and LCM:

Problem: Find the GCD and LCM of 12 and 18.

Solution: 1. Finding the GCD: - Using the Euclidean algorithm: - Divide 18 by 12: 18 = 1 * 12 + 6 - Divide 12 by 6: 12 = 2 * 6 + 0 - The GCD of 12 and 18 is the last non-zero remainder, which is 6.

2. Finding the LCM: - LCM(12, 18) = (12 * 18) / GCD(12, 18) = (12 * 18) / 6 = 36

Therefore, the GCD of 12 and 18 is 6, and the LCM is 36.

Additional Examples

Here are a few more examples of finding the GCD and LCM:

1. Find the GCD and LCM of 24 and 36: - GCD(24, 36) = 12 - LCM(24, 36) = 72

2. Find the GCD and LCM of 15 and 25: - GCD(15, 25) = 5 - LCM(15, 25) = 75

3. Find the GCD and LCM of 8 and 12: - GCD(8, 12) = 4 - LCM(8, 12) = 24

I hope this helps! Let me know if you have any further questions.

Answer 3

НОК (наименьшее общее кратное) - это наименьшее число, которое делится без остатка на все числа, для которых ищется НОК.

НОД (наибольший общий делитель) - это наибольшее число, на которое делятся все числа, для которых ищется НОД.

Примеры:

1) Найти НОК и НОД для чисел 6 и 8.

Для чисел 6 и 8 НОК будет равен 24, а НОД - 2.

2) Найти НОК и НОД для чисел 12 и 18.

Для чисел 12 и 18 НОК будет равен 36, а НОД - 6.

3) Найти НОК и НОД для чисел 15 и 25.

Для чисел 15 и 25 НОК будет равен 75, а НОД - 5.

Взаимно простые числа - это числа, у которых НОД равен 1, то есть они не имеют общих делителей, кроме 1.

Общее кратное можно найти, умножив все простые множители чисел, для которых ищется НОК, взяв их максимальные степени. Например, для чисел 6 и 8, их НОК будет равен 2^3 * 3.