Question

Три спортсмена бегут по круговому стадиону в одном направлении, стартовав одновременно. Первый пробегает круг за 132 секунды, второй - за 106, и третий - за 134. Через сколько секунд после старта они все впервые одновременно окажутся в точке старта

Answer 1

Одновременно они встретятся через такое количество минут, которое нацело делится на все три числа,
то есть надо найти НОК{132,106,134}

132= 2*66
106=2*53
134 = 2*67
НОК = 132*53*67 = 106*66*67=134*66*53 = 468732с ≈        ≈ 7812мин ≈ 130час
(нереальное здоровье у спортсменов, такого же и составителю задач)

Answer 2

Calculating the Time When They Meet at the Starting Point

To find out when the three athletes will meet at the starting point, we can use the concept of the least common multiple (LCM) of the three times it takes for each athlete to complete one lap around the circular track.

- The first athlete completes a lap in 132 seconds. - The second athlete completes a lap in 106 seconds. - The third athlete completes a lap in 134 seconds.

Calculating the Least Common Multiple (LCM)

The LCM of the given numbers can be calculated using various methods, such as prime factorization, listing multiples, or using the division method. Let's calculate the LCM using the division method.

The LCM of 132, 106, and 134 can be calculated as follows:

1. Prime Factorization: - Prime factorization of 132: 2^2 * 3 * 11 - Prime factorization of 106: 2 * 53 - Prime factorization of 134: 2 * 67

2. Using Division Method: - LCM(132, 106, 134) = 2 * 2 * 3 * 11 * 53 * 67 - LCM(132, 106, 134) = 15708 seconds

Therefore, the three athletes will meet at the starting point for the first time after 15708 seconds.