Question

Объясните пожалуйста Как искать НОК и НОД,что на что умножать

Answer 1

Вы же изучали разложение на простые множители ? так вот нужно разложить 2 числа к примеру 45 и 15 ( нод ) 45\5\9\3\3\1 15\5\3\3\1 общие цифры тут 5 и 3 получается нод ( 45 15 ) = 5*3=15 а чтобы найти нок этих чисел нужно сделать так нок ( 45 15 ) = 5*3*9*3 = 405 нод переводится как НАИБОЛЬШИЙ ОБЩИЙ ДЕЛИТЕЛЬ а нок как НАИМЕНЬШЕЕ ОБЩЕЕ КРАТНОЕ

Answer 2

Finding the Greatest Common Divisor (GCD) and Least Common Multiple (LCM)

To find the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two numbers, you can use different methods. The GCD is the largest positive integer that divides each of the numbers without leaving a remainder, while the LCM is the smallest multiple that is exactly divisible by each of the numbers.

Finding the Greatest Common Divisor (GCD): To find the GCD of two numbers, you can use methods such as prime factorization, Euclidean algorithm, or using the GCD formula.

Prime Factorization Method: 1. Express each number as a product of prime factors. 2. Identify the common prime factors and multiply them together to find the GCD.

Euclidean Algorithm: 1. Divide the larger number by the smaller number. 2. Replace the larger number with the smaller number and the smaller number with the remainder. 3. Repeat the process until the remainder is 0. The divisor at this step is the GCD.

Using the GCD Formula: The GCD of two numbers a and b can be calculated using the formula: GCD(a, b) = GCD(b, a % b), where % represents the modulo operation.

Finding the Least Common Multiple (LCM): To find the LCM of two numbers, you can use methods such as prime factorization or the LCM formula.

Prime Factorization Method: 1. Express each number as a product of prime factors. 2. Identify the highest power of each prime factor that appears in the factorization of the numbers and multiply them together to find the LCM.

LCM Formula: The LCM of two numbers a and b can be calculated using the formula: LCM(a, b) = (a * b) / GCD(a, b).

In summary, to find the GCD and LCM of two numbers, you can use methods such as prime factorization, the Euclidean algorithm, and specific formulas for GCD and LCM calculations.

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