Question

Найти НОК 856;214;107. С решением

Answer 1

856=2*2*2*107
214=2*107
107=107

Все множители 107 вошли во множители 856, так же множители 214 вошли во множители 856
значит НОК(856;214;107)= 856

Answer 2

Finding the Least Common Multiple (LCM) of 856, 214, and 107

To find the Least Common Multiple (LCM) of three numbers, we need to determine the smallest number that is divisible by all three numbers. In this case, we need to find the LCM of 856, 214, and 107.

To calculate the LCM, we can use the prime factorization method 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. Keep dividing until you can no longer divide evenly. - 856 ÷ 2 = 428 - 214 ÷ 2 = 107 - 107 ÷ 2 = 53

2. Now, divide the remaining numbers by the next smallest prime number, which is 3. Again, keep dividing until you can no longer divide evenly. - 428 ÷ 2 = 214 - 214 ÷ 2 = 107 - 107 ÷ 2 = 53

3. Repeat this process for the next prime numbers, which are 5, 7, 11, and so on, until you reach a prime number greater than the largest number in the list.

Using this method, we find that the prime factorization of the given numbers is as follows: - 856 = 2^3 * 107 - 214 = 2 * 107 - 107 = 107

To find the LCM, we take the highest power of each prime factor that appears in the factorization of any of the numbers. In this case, the LCM is calculated as follows:

LCM = 2^3 * 107 = 8 * 107 = 856

Therefore, the LCM of 856, 214, and 107 is 856.