Question

Найдите НОД и НОК чисел 742 и 795

Answer 1

Раскладываем числа на простые:
742= 2*7*53
795=3*5*53
НОД = 53
НОК = 11130

Answer 2

Finding the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of 742 and 795

To find the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of 742 and 795, we can use the following formulas:

GCD Formula: The GCD of two numbers a and b is denoted as GCD(a, b) and can be calculated using the Euclidean algorithm.

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

Let's calculate the GCD and LCM of 742 and 795 using the above formulas.

Calculating the Greatest Common Divisor (GCD)

The GCD of 742 and 795 can be calculated using the Euclidean algorithm.

The Euclidean algorithm states that the GCD of two numbers a and b is the same as the GCD of b and the remainder when a is divided by b. This process is repeated until the remainder is 0.

Using the Euclidean algorithm: - GCD(742, 795) = GCD(795, 742 % 795) - GCD(795, 742 % 795) = GCD(795, 742)

Calculating the Least Common Multiple (LCM)

The LCM of 742 and 795 can be calculated using the formula LCM(a, b) = (a * b) / GCD(a, b).

Let's calculate the LCM using the GCD we found.

Results: - GCD(742, 795) = 1 - LCM(742, 795) = (742 * 795) / GCD(742, 795) = 742 * 795

So, the GCD of 742 and 795 is 1 and the LCM of 742 and 795 is 742 * 795.

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