Question

Найдите НОК (35, 60, 90)​

Answer 1

Ответ:

Пошаговое объяснение:

1) Разложим числа на простые множетели:

90 = 2 * 3 * 3 * 5

35 = 5 * 7

60 = 2 * 2 * 3 * 5

2) Найдём и подчеркнем множители в разложении меньших чисел которые не вошли в разложение наибольшего числа:

90 = 2 * 3 * 3 * 5

35 = 5 * 7

60 = 2 * 2 * 3 * 5

3) Теперь недостающие множители добавим к множителям большего числа и перемножим их:

НОК (35; 60; 90) = 2 * 3 * 3 * 5 * 7 * 2 = 1260

Ответ: НОК (35; 60; 90) = 1260

Answer 2

Finding the Least Common Multiple (LCM) of (35, 60, 90)

To find the least common multiple (LCM) of the numbers 35, 60, and 90, we can use the prime factorization method. First, we'll find the prime factorization of each number, and then we'll take the highest power of all the prime factors to calculate the LCM.

Prime Factorization of the Numbers: - 35: 35 = 5 * 7 - 60: 60 = 2^2 * 3 * 5 - 90: 90 = 2 * 3^2 * 5

Calculating the LCM: The LCM is the product of the highest powers of all prime factors involved. Therefore, the LCM of 35, 60, and 90 is: LCM(35, 60, 90) = 2^2 * 3^2 * 5 * 7 = 2 * 2 * 3 * 3 * 5 * 7 = 2 * 2 * 3 * 3 * 5 * 7 = 2 * 3 * 2 * 3 * 5 * 7 = 2 * 3 * 2 * 3 * 5 * 7 = 6 * 3 * 5 * 7 = 90 * 35 = 3150

Therefore, the least common multiple (LCM) of 35, 60, and 90 is 3150.