Question

НОД(504,756)=НОК(504,756)=

Answer 1

Ответ:НОК(504;756)=1512

Пошаговое объяснение:

504=2³*3²*7

756=2²*3³*7

НОК=2³*3³*7=1512

Answer 2

To find the greatest common divisor (GCD) and least common multiple (LCM) of two numbers, 504 and 756, we can use the following steps:

Step 1: Find the GCD (НОД) of 504 and 756. Step 2: Find the LCM (НОК) of 504 and 756.

Step 1: Find the GCD (НОД) of 504 and 756: The GCD is the largest positive integer that divides both numbers without leaving a remainder. We can use the Euclidean algorithm to find the GCD.

Euclidean Algorithm:

1. Divide the larger number by the smaller number.
2. Set the larger number to the divisor and the smaller number to the remainder.
3. Repeat steps 1 and 2 until the remainder is 0.
4. The last non-zero remainder is the GCD.

Let's apply the Euclidean algorithm:

Step 1: 756 ÷ 504 = 1 with a remainder of 252 Step 2: 504 ÷ 252 = 2 with a remainder of 0

The last non-zero remainder is 252, so the GCD of 504 and 756 is 252.

Step 2: Find the LCM (НОК) of 504 and 756: The LCM is the smallest positive integer that is divisible by both numbers.

LCM = (504 * 756) / GCD LCM = (504 * 756) / 252 LCM = 381024 / 252 LCM = 1512

So, the GCD(504, 756) = 252, and the LCM(504, 756) = 1512.