Question

Как находить НОК И НОД чисел срочно

Answer 1

Разложите оба числа на простые множители.
По аналогии с теорией множеств, НОД - это пересечение множеств, НОК - их объединение. (a^b считаем подмножеством набора a^c когда b<=c)

Answer 2

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

To find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of two numbers, you can use different methods such as prime factorization, the division method, or the Euclidean algorithm. Here's a brief explanation of each method:

1. Prime Factorization Method: - To find the LCM and GCD using the prime factorization method, you need to factorize each number into its prime factors and then use the common and uncommon prime factors to calculate the LCM and GCD respectively.

2. Division Method: - The division method involves dividing the larger number by the smaller number and then using the remainder to repeat the process until the remainder becomes zero. The last divisor is the GCD, and the LCM can be calculated using the formula: LCM = (Number1 * Number2) / GCD.

3. Euclidean Algorithm: - The Euclidean algorithm is an efficient method to find the GCD of two numbers. It involves repeatedly applying the division algorithm to find the GCD.

Now, let's use the provided examples to demonstrate the calculation of LCM and GCD using the prime factorization method.

For the numbers (24, 36): - Prime factorization of 24: 24 = 2 * 2 * 2 * 3 - Prime factorization of 36: 36 = 2 * 2 * 3 * 3 - LCM(24, 36) = 2 * 2 * 2 * 3 * 3 = 72 - GCD(24, 36) = 2 * 2 * 3 = 12 For the numbers (315, 245): - Prime factorization of 315: 315 = 5 * 3 * 3 * 7 - Prime factorization of 245: 245 = 5 * 7 * 7 - LCM(315, 245) = 5 * 3 * 3 * 7 * 7 = 11025 - GCD(315, 245) = 5 * 7 = 35 For the numbers (236, 328): - Prime factorization of 236: 236 = 2 * 2 * 59 - Prime factorization of 328: 328 = 2 * 2 * 2 * 41 - LCM(236, 328) = 2 * 2 * 59 * 2 * 41 = 19352 - GCD(236, 328) = 2 * 2 = 4 These examples demonstrate how to find the LCM and GCD using the prime factorization method. If you have specific numbers for which you want to find the LCM and GCD, feel free to provide them for a detailed calculation using a specific method.