Question

НОК(150; 375; 600)???

Answer 1

Разложим числа на простые множители. Сначала запишем разложение на множители самого большого число, затем остальные числа. Подчеркнем в разложении меньших чисел множители, которые не вошли в разложение наибольшего числа.
150 = 2 * 3 * 5 * 5
375 = 3 * 5 * 5 * 5
600 = 2 * 2 * 2 * 3 * 5 * 5
Чтобы найти НОК, нужно чтобы использовались все множители:
150: имеем 1 - "2", 1 - "3", 2 - "5"
375: имеем 1 - "3", 3 - "5"
600: имеем 3 - "2", 2 - "3", 2 - "5"
В НОК будет: 3 -"2", 1 - "3", 3 - "5"
 2 * 2 * 2 * 3 * 5 * 5 * 5 = 3000

Answer 2

To find the least common multiple (LCM) of three numbers, you can use the following steps:

Step 1: Find the prime factors of each number. Step 2: Identify the highest power of each prime factor that appears in any of the numbers. Step 3: Multiply all the prime factors, each raised to its highest power.

Let's find the LCM of 150, 375, and 600:

Step 1: Prime factorization of each number:

• 150 = 2 * 3 * 5^2
• 375 = 3 * 5^3
• 600 = 2^3 * 3 * 5^2

Step 2: Identify the highest power of each prime factor:

• The highest power of 2 is 2^3 (from 600).
• The highest power of 3 is 3 (from both 150 and 375).
• The highest power of 5 is 5^3 (from 375).

Step 3: Multiply all the prime factors, each raised to its highest power: LCM(150, 375, 600) = 2^3 * 3 * 5^3 = 8 * 3 * 125 = 3000

So, the least common multiple of 150, 375, and 600 is 3000.