Question

НОД(123,82)=. НОК(20,70,15)=.

Answer 1

Ответ:

41;420

Объяснение:

Разложим 123 на простые и сложные множители 2 и 41 и 3 и 41

41 - одинаковый множитель в обоих числах

Разложим 20,70,и 15 на простые и сложные знаменатели

20 - 2,2,5

70 - 2,5,7

15 - 3,5

Нок - 2*3*2*5*7 =420

Answer 2

The greatest common divisor (НОД) of two numbers is the largest positive integer that divides both of them without leaving a remainder.

The least common multiple (НОК) of a set of numbers is the smallest positive integer that is evenly divisible by all the numbers in the set.

Let's calculate:

1. НОД(123, 82): To find the greatest common divisor of 123 and 82, you can use various methods like prime factorization, Euclidean algorithm, or a calculator.

Using the Euclidean algorithm:

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gcd(123, 82) = gcd(82, 123 % 82) = gcd(82, 41) = gcd(41, 82 % 41) = gcd(41, 0) = 41

So, НОД(123, 82) = 41.

2. НОК(20, 70, 15): To find the least common multiple of 20, 70, and 15, you can use the prime factorization method.

Prime factorization:

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20 = 2^2 * 5
70 = 2 * 5 * 7
15 = 3 * 5

The least common multiple is the product of the highest powers of all prime factors involved:

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НОК(20, 70, 15) = 2^2 * 3 * 5 * 7 = 420

So, НОК(20, 70, 15) = 420.