Question

1. Знайдіть НСК чисел: а) 12 і 24; б) 75 і 45; в) 81 і 243. Чи є серед них взаємно прості?

Answer 1

Відповідь:

а) 24, б) 225, в) 243

Покрокове пояснення:

а) НСК 24 і 12 = 24, бо 24 ділиться на 12 і на себе

б) НСК 75 і 45 = 225

в) НСК 243 і 81 = 243, бо 243 ділиться на 81 і на себе

Взаємно простих чисел немає

Answer 2

Finding the GCD (НСК) of Numbers

To find the greatest common divisor (НСК) of two numbers, we can use the Euclidean algorithm. The Euclidean algorithm states that the GCD of two numbers is equal to the GCD of the remainder when the larger number is divided by the smaller number, until the remainder becomes zero.

Let's apply the Euclidean algorithm to the given numbers:

a) 12 and 24: To find the GCD of 12 and 24, we divide 24 by 12, which gives us a remainder of 0. Therefore, the GCD of 12 and 24 is 12.

b) 75 and 45: To find the GCD of 75 and 45, we divide 75 by 45, which gives us a remainder of 30. Then, we divide 45 by 30, which gives us a remainder of 15. Finally, we divide 30 by 15, which gives us a remainder of 0. Therefore, the GCD of 75 and 45 is 15.

c) 81 and 243: To find the GCD of 81 and 243, we divide 243 by 81, which gives us a remainder of 0. Therefore, the GCD of 81 and 243 is 81.

Are They Relatively Prime?

To determine if two numbers are relatively prime, we need to check if their greatest common divisor (GCD) is 1. If the GCD is 1, then the numbers are relatively prime or mutually prime.

Let's check if the given pairs of numbers are relatively prime:

a) 12 and 24: The GCD of 12 and 24 is 12, which is not equal to 1. Therefore, 12 and 24 are not relatively prime.

b) 75 and 45: The GCD of 75 and 45 is 15, which is not equal to 1. Therefore, 75 and 45 are not relatively prime.

c) 81 and 243: The GCD of 81 and 243 is 81, which is not equal to 1. Therefore, 81 and 243 are not relatively prime.

In conclusion, none of the given pairs of numbers are relatively prime.

Note: The sources provided did not contain specific information about finding the GCD of numbers or determining if they are relatively prime. However, the information provided is based on the well-known Euclidean algorithm and the definition of relatively prime numbers.