Question

НОК 9 12 24, решите пожалуйста, ответ должен быть 72! С полным объяснением. ​

Answer 1

Задание:

Найдите НОК чисел 9, 12, 24.

Ответ:

НОК (9; 12; 24) = 72.

Пошаговое объяснение:

Разложим числа 9, 12, 24 на простые множители:

9 | 3                 12 | 2                     24 | 2

3 | 3                  6 | 2                      12 | 2

1  |                     3 | 3                        6 | 2

                         1 |                            3 | 3

                                                         1 |

Запишем множители первого числа 9 и допишем недостающие чисел 12 и 24 (2³):

3 × 3 × 2 × 2 × 2 = 72.

Записываем ответ.

Answer 2

Finding the Least Common Multiple (LCM) of 9, 12, and 24

To find the least common multiple (LCM) of 9, 12, and 24, we need to determine the smallest number that is divisible by all three numbers.

One way to find the LCM is by listing the multiples of each number until we find a common multiple. Let's start with the number 9:

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, ...

Next, let's list the multiples of 12:

Multiples of 12: 12, 24, 36, 48, 60, 72, ...

Finally, let's list the multiples of 24:

Multiples of 24: 24, 48, 72, ...

From the lists above, we can see that the smallest number divisible by all three numbers is 72. Therefore, the LCM of 9, 12, and 24 is 72.

Explanation:

The LCM is the smallest multiple that is divisible by all the given numbers. In this case, we found that 72 is the smallest number that is divisible by 9, 12, and 24.

To verify this, we can check that 72 is indeed divisible by all three numbers:

- 72 divided by 9 equals 8. - 72 divided by 12 equals 6. - 72 divided by 24 equals 3.

Since all the divisions result in whole numbers, we can conclude that 72 is indeed divisible by 9, 12, and 24.

I hope this explanation helps! Let me know if you have any further questions.