Question

НОК(3,8,4)НОД(3,8,4)НОК(7,10,3)НОД(7,10,3)​

Answer 1

3 - простое число

8 = 2³

4 = 2²

НОК (3; 8 и 4) = 2³ · 3 = 24 - наименьшее общее кратное

НОД (3; 8 и 4) = 1 - наибольший общий делитель

Числа 3, 8 и 4 взаимно простые, так как у них нет общих делителей, кроме единицы.

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7 и 3 - простые числа

10 = 2 · 5

НОК (7; 10 и 3) = 2 · 3 · 5 · 7 = 210 - наименьшее общее кратное

НОД (7; 10 и 3) = 1 - наибольший общий делитель

Числа 7, 10 и 3 взаимно простые, так как у них нет общих делителей, кроме единицы.

Answer 2

To calculate the least common multiple (LCM) and greatest common divisor (GCD) of the given numbers, we can use the following formulas:

LCM(a, b, c) = LCM(LCM(a, b), c) GCD(a, b, c) = GCD(GCD(a, b), c)

Let's calculate the values step by step:

Step 1: Calculate LCM(3, 8) and GCD(3, 8) To calculate the LCM, we find the smallest multiple that both 3 and 8 divide evenly into, which is 24. To calculate the GCD, we find the largest number that divides both 3 and 8 without leaving a remainder, which is 1. Therefore, LCM(3, 8) = 24 and GCD(3, 8) = 1.

Step 2: Calculate LCM(24, 4) and GCD(24, 4) To calculate the LCM, we find the smallest multiple that both 24 and 4 divide evenly into, which is 24. To calculate the GCD, we find the largest number that divides both 24 and 4 without leaving a remainder, which is 4. Therefore, LCM(24, 4) = 24 and GCD(24, 4) = 4.

Step 3: Calculate LCM(7, 10) and GCD(7, 10) To calculate the LCM, we find the smallest multiple that both 7 and 10 divide evenly into, which is 70. To calculate the GCD, we find the largest number that divides both 7 and 10 without leaving a remainder, which is 1. Therefore, LCM(7, 10) = 70 and GCD(7, 10) = 1.

Step 4: Calculate LCM(70, 3) and GCD(70, 3) To calculate the LCM, we find the smallest multiple that both 70 and 3 divide evenly into, which is 210. To calculate the GCD, we find the largest number that divides both 70 and 3 without leaving a remainder, which is 1. Therefore, LCM(70, 3) = 210 and GCD(70, 3) = 1.

Finally, we have: LCM(3, 8, 4) = LCM(LCM(3, 8), 4) = LCM(24, 4) = 24 GCD(3, 8, 4) = GCD(GCD(3, 8), 4) = GCD(1, 4) = 1 LCM(7, 10, 3) = LCM(LCM(7, 10), 3) = LCM(70, 3) = 210 GCD(7, 10, 3) = GCD(GCD(7, 10), 3) = GCD(1, 3) = 1

Therefore: LCM(3, 8, 4) = 24 GCD(3, 8, 4) = 1 LCM(7, 10, 3) = 210 GCD(7, 10, 3) = 1