Question

У ящику лежить певна кількість яблук. Виявилося, що їх можна розкласти в 5 однакових рядів, або у 8 однакових рядів, або в 12 однакових рядів. Яка найменша кількість яблук може бути в ящику?

Answer 1

Відповідь:

120

Покрокове пояснення:

У меня тест был такой-же

Answer 2

Problem Analysis

We are given that there is a certain number of apples in a box. These apples can be arranged in 5 equal rows, 8 equal rows, or 12 equal rows. We need to determine the smallest possible number of apples in the box.

Solution

To find the smallest possible number of apples in the box, we need to find the least common multiple (LCM) of 5, 8, and 12. The LCM is the smallest number that is divisible by all three numbers.

The LCM of 5, 8, and 12 is 120. Therefore, the smallest possible number of apples in the box is 120.

Explanation

To understand why 120 is the smallest possible number of apples in the box, let's consider the factors of each number:

- Factors of 5: 1, 5 - Factors of 8: 1, 2, 4, 8 - Factors of 12: 1, 2, 3, 4, 6, 12

To find the LCM, we need to find the smallest number that contains all the factors of each number. In this case, the LCM is 2 * 2 * 2 * 3 * 5 = 120.

By arranging 120 apples in 5 equal rows, we would have 24 apples in each row. Similarly, arranging 120 apples in 8 equal rows or 12 equal rows would also result in 15 apples in each row.

Therefore, the smallest possible number of apples in the box is 120, which can be arranged in 5, 8, or 12 equal rows with 24, 15, or 10 apples in each row, respectively.

Conclusion

The smallest possible number of apples in the box is 120.