Question

Найти НОК 120;300;100

Answer 1

120 = 2³ · 3 · 5
300 = 2² · 3 · 5²
100 = 2² · 5²
2³ · 3 · 5² = 600

Вот

Answer 2

$120= 2^{3} * 3*5 \\ 100= 2^{2}*5^{2} \\ 300=2^{2}*3*5^{2}$
НОК(120, 100, 300)=$2^{3}*3* 5^{2}=600$

Answer 3

Finding the Least Common Multiple (LCM) of 120, 300, and 100

To find the least common multiple (LCM) of 120, 300, and 100, we can use different methods such as prime factorization or the division method. Let's use the division method to find the LCM.

1. Start by dividing each number by the smallest prime number, which is 2: - 120 divided by 2 is 60. - 300 divided by 2 is 150. - 100 divided by 2 is 50.

2. Next, divide the resulting numbers by the smallest prime number again, which is 2: - 60 divided by 2 is 30. - 150 divided by 2 is 75. - 50 divided by 2 is 25.

3. Repeat this process until you can no longer divide the numbers by 2: - 30 divided by 2 is 15. - 75 divided by 3 is 25.

4. Now, divide the remaining numbers by the next smallest prime number, which is 3: - 15 divided by 3 is 5.

5. Finally, divide the remaining number by itself: - 5 divided by 5 is 1.

To find the LCM, multiply all the divisors together: 2 * 2 * 2 * 3 * 5 * 5 * 1 = 600.

Therefore, the LCM of 120, 300, and 100 is 600.