Question

Найти НОК и НОД для чисел 156 и 390​

Answer 1

Ответ:

НОД (156; 390) = 2 • 3 • 13 = 78

НОК (156, 390) = 2 • 3 • 5 • 13 • 2 = 780

Пошаговое объяснение:

Answer 2

Finding the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 156 and 390

To find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 156 and 390, we can use the following methods:

Greatest Common Divisor (GCD): The greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder.

Least Common Multiple (LCM): The least common multiple (LCM) of two numbers is the smallest multiple that is exactly divisible by both numbers.

Now, let's calculate the GCD and LCM for the given numbers.

Calculating the Greatest Common Divisor (GCD)

The GCD of 156 and 390 can be calculated using various methods, such as prime factorization, Euclidean algorithm, or using a GCD calculator.

Using the Euclidean algorithm: 1. Start with the two numbers, 156 and 390. 2. Divide the larger number by the smaller number and take the remainder. 3. Replace the larger number with the smaller number and the smaller number with the remainder. 4. Repeat the process until the remainder is 0. The last non-zero remainder is the GCD.

Using the Euclidean algorithm, the GCD of 156 and 390 is 78.

Calculating the Least Common Multiple (LCM)

The LCM of 156 and 390 can be calculated using the prime factorization method or by finding the product of the numbers divided by their GCD.

Using the prime factorization method: 1. Find the prime factorization of each number. 2. Multiply the highest powers of all prime factors to find the LCM.

The LCM of 156 and 390 is 1560.

Therefore, the GCD of 156 and 390 is 78, and the LCM of 156 and 390 is 1560.