Question

Решить(с помощью НОД ;НОК)Для учащихся 1 класса приготовили одинаковые подарки.Во всех подарках было 120 шок. 280 конф. и 320 орехов. Сколько всего учащихся в этом классе?СРОЧНО!!!!!!!!!!!!!!СПАСАЙТЕ!!!!!!!

Answer 1

120 = (2*2*2) * 3 * 5
280 = (2*2*2) * 5 * 7
320 = (2*2*2*2*2*2) * 5
НОД = (2*2*2) * 5 = 40 - наибольший общий делитель
120 : 40 = 3 шоколадки
280 : 40 = 7 конфет
320 : 40 = 8 орехов
Ответ: 40 учащихся в классе. В каждом подарке по 3 шоколадки, 7 конфет и 8 орехов.

Answer 2

Problem Analysis

To solve this problem, we need to find the total number of students in the class. We are given that each student received the same number of gifts, which contained 120 chocolates, 280 candies, and 320 nuts. We can use the concepts of the greatest common divisor (GCD) and least common multiple (LCM) to find the total number of students.

Solution

To find the total number of students, we can use the concept of the least common multiple (LCM). The LCM of three numbers is the smallest number that is divisible by all three numbers.

Let's find the LCM of 120, 280, and 320.

The prime factorization of 120 is 2^3 * 3 * 5. The prime factorization of 280 is 2^3 * 5 * 7. The prime factorization of 320 is 2^6 * 5.

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers. So the LCM of 120, 280, and 320 is 2^6 * 3 * 5 * 7 = 2240.

Therefore, there are 2240 students in the class.

Verification

Let's verify the solution by checking if the LCM of 120, 280, and 320 is indeed 2240.

The LCM of 120, 280, and 320 can be calculated by finding the LCM of 120 and 280, and then finding the LCM of the result and 320.

The LCM of 120 and 280 is 840. The LCM of 840 and 320 is 2240.

Therefore, the solution is verified.

Conclusion

The total number of students in the class is 2240.