Question

Найдите Нок 280 140 224

Answer 1

Ответ: НОК этих чисел 1120

Answer 2

Нок (наименьшее общее кратное) для чисел 280, 140 и 224 равно 1120 [[1]](https://nonano.ru/naimenshee-obshchee-kratnoe-chisel-nok-chisel?start=280-140-224).

Calculation of the Least Common Multiple (LCM)

To find the LCM of three numbers, we can use the prime factorization method or the division method. Let's use the division method to calculate the LCM of 280, 140, and 224.

1. Start by dividing each number by its smallest prime factor: - 280 ÷ 2 = 140 - 140 ÷ 2 = 70 - 224 ÷ 2 = 112

2. Divide the resulting numbers by their smallest prime factors: - 140 ÷ 2 = 70 - 70 ÷ 2 = 35 - 112 ÷ 2 = 56

3. Divide the remaining numbers by their smallest prime factors: - 70 ÷ 5 = 14 - 35 ÷ 5 = 7 - 56 ÷ 2 = 28

4. Divide the remaining numbers by their smallest prime factors: - 14 ÷ 2 = 7 - 7 ÷ 7 = 1 - 28 ÷ 2 = 14

5. Divide the remaining numbers by their smallest prime factors: - 7 ÷ 7 = 1 - 14 ÷ 2 = 7

6. The remaining numbers are all equal to 1, which means we have finished dividing.

7. Multiply all the prime factors together: - 2 × 2 × 2 × 2 × 5 × 7 = 1120

Therefore, the LCM of 280, 140, and 224 is 1120.

Answer: The least common multiple (LCM) of 280, 140, and 224 is 1120.