Question

Три друга встретились в компьютерном клубе. Через какое наименьшее время повторится их встреча, если один из них ходит туда 1 раз в 5 дней , второй – раз в 12 дней , третий – раз в 10 дней? Решить задачу с РЕШЕНИЕМ!!!!!!!

Answer 1

Как то так как то так как то так

Answer 2

Problem Analysis

Three friends meet at a computer club, and we need to find the minimum time it takes for their meeting to repeat, given that one friend goes there every 5 days, the second goes every 12 days, and the third goes every 10 days.

Solution

To find the minimum time for their meeting to repeat, we need to find the least common multiple (LCM) of the three numbers: 5, 12, and 10.

The LCM of 5, 12, and 10 is the smallest number that is a multiple of all three numbers.

Calculation

The LCM of 5, 12, and 10 can be calculated using the following steps: 1. Find the prime factorization of each number. 2. Take the highest power of all prime factors present in the numbers.

Prime Factorization

- Prime factorization of 5: 5 - Prime factorization of 12: 2^2 * 3 - Prime factorization of 10: 2 * 5

LCM Calculation

The LCM of 5, 12, and 10 is calculated as follows: - The highest power of 2 is 2^2. - The highest power of 3 is 3. - The highest power of 5 is 5.

So, the LCM of 5, 12, and 10 is 2^2 * 3 * 5 = 60.

Therefore, the minimum time for their meeting to repeat is 60 days.

Conclusion

The three friends will meet again at the computer club after 60 days, which is the least common multiple of the intervals at which they visit the club.