Question

как наити НОК правило с примером

Answer 1

Чтобы найти НОК 2-х чисел, нужно каждое из них разложить на простые множители (есть алгоритм), а потом 1е число умножить на недостающие множители из разложения 2го (3го, 4го и т.д.). Если два числа взаимно просты (нет общих множителей, кроме 1), то их НОК равно их произведению. 

Пример 1: найти НОК (12, 18) 
12 = 2*2*3, 18 = 2*3*3 => НОК(12,13) = (2*2*3)*3 (в разложении числа 12 нет второй тройки, которая есть в разложении числа 18). 
Пример 2: найти НОК (10, 9) 
10=2*5, 9=3*3 - взаимно просты => НОК(10,9)=10*9=90

Answer 2

Finding the Least Common Multiple (LCM)

The Least Common Multiple (LCM) is the smallest multiple that two or more numbers have in common. To find the LCM, you can use different methods, such as prime factorization or the ladder method. Here, I will explain how to find the LCM using the prime factorization method.

1. Prime Factorization Method: - Step 1: Prime factorize each number. - Step 2: Write down all the prime factors with their highest powers. - Step 3: Multiply the prime factors with their highest powers to find the LCM.

Let's look at an example to understand this method better.

Example: Find the LCM of 315 and 245.

1. Prime factorize each number: - 315 = 5 * 3 * 3 * 7 - 245 = 5 * 7 * 7

2. Write down all the prime factors with their highest powers: - 315 = 5 * 3^2 * 7 - 245 = 5 * 7^2

3. Multiply the prime factors with their highest powers to find the LCM: - LCM(315, 245) = 5 * 3^2 * 7^2 = 5 * 9 * 49 = 2205

Therefore, the LCM of 315 and 245 is 2205.

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