Question

Найдите НОК(24; 42), НОК( 15; 65); НОК(62;84) , НОК(35;105), НОК( 28; 84).​

Answer 1

Ответ:

Пошаговое объяснение:

1)Разложим  на простые множители 42 и 24

42 = 2 · 3 · 7

24 = 2 · 2 · 2 · 3

Чтобы определить НОК, необходимо недостающие множители добавить к множителям большего числа и перемножить их:

НОК (24; 42) = 2 · 3 · 7 · 2 · 2 = 168

2)

65 = 5 · 13

15 = 3 · 5

НОК (15; 65) = 5 · 13 · 3 = 195

3)

84 = 2 · 2 · 3 · 7

62 = 2 · 31

НОК (62; 84) = 2 · 2 · 3 · 7 · 31 = 2604

4)

105 = 3 · 5 · 7

35 = 5 · 7

НОК (35; 105) = 3 · 5 · 7 = 105

5)

84 = 2 · 2 · 3 · 7

28 = 2 · 2 · 7

НОК (28; 84) = 2 · 2 · 3 · 7 = 84

Answer 2

Calculating the Least Common Multiple (НОК)

To calculate the least common multiple (НОК) of the given numbers, we can use the prime factorization method. The least common multiple of two numbers is the smallest number that is a multiple of both numbers.

1. НОК(24, 42): - First, we find the prime factorization of each number: - 24 = 2^3 * 3^1 - 42 = 2^1 * 3^1 * 7^1 - Then, we take the highest power of each prime factor: - НОК(24, 42) = 2^3 * 3^1 * 7^1 = 168.

2. НОК(15, 65): - Prime factorization: - 15 = 3^1 * 5^1 - 65 = 5^1 * 13^1 - Highest power of each prime factor: - НОК(15, 65) = 3^1 * 5^1 * 13^1 = 195.

3. НОК(62, 84): - Prime factorization: - 62 = 2^1 * 31^1 - 84 = 2^2 * 3^1 * 7^1 - Highest power of each prime factor: - НОК(62, 84) = 2^2 * 3^1 * 7^1 * 31^1 = 2604.

4. НОК(35, 105): - Prime factorization: - 35 = 5^1 * 7^1 - 105 = 3^1 * 5^1 * 7^1 - Highest power of each prime factor: - НОК(35, 105) = 3^1 * 5^1 * 7^1 = 105.

5. НОК(28, 84): - Prime factorization: - 28 = 2^2 * 7^1 - 84 = 2^2 * 3^1 * 7^1 - Highest power of each prime factor: - НОК(28, 84) = 2^2 * 3^1 * 7^1 = 84.

These are the least common multiples for the given numbers.