Question

Найдите НОД и НОК чисел 588 252

Answer 1

НОД588=588=2(во второй степени)х(умножить)147
НОД252=252=2(во второй степени)х3(во второй степени)х7

Answer 2

Calculation of GCD and LCM

To find the greatest common divisor (GCD) and least common multiple (LCM) of the numbers 588 and 252, we can use various methods such as prime factorization, division method, or the Euclidean algorithm. Let's use the Euclidean algorithm, which is an efficient method for calculating the GCD.

The Euclidean algorithm works by repeatedly dividing the larger number by the smaller number and replacing the larger number with the remainder until the remainder becomes zero. The last non-zero remainder is the GCD of the two numbers.

Here's how we can apply the Euclidean algorithm to find the GCD of 588 and 252:

1. Divide 588 by 252: 588 ÷ 252 = 2 with a remainder of 84. 2. Divide 252 by 84: 252 ÷ 84 = 3 with a remainder of 0.

Since the remainder has become zero, the GCD of 588 and 252 is the last non-zero remainder, which is 84.

To find the least common multiple (LCM), we can use the formula:

LCM(a, b) = (a * b) / GCD(a, b)

Substituting the values of a = 588, b = 252, and GCD(a, b) = 84, we can calculate the LCM:

LCM(588, 252) = (588 * 252) / 84 = 1764.

Therefore, the GCD of 588 and 252 is 84, and the LCM is 1764.

Answer

The greatest common divisor (GCD) of 588 and 252 is 84, and the least common multiple (LCM) is 1764.