Question

НОД (32;78)= НОК (32;78)=

Answer 1

32 : 2 = 16

16 : 2 = 8

8 : 2 = 4

4 : 2 = 2

2 : 2 = 1

32 = 2⁵ - простые множители числа

- - - - - - -

78 : 2 = 39

39 : 3 = 13

13 : 13 = 1

78 = 2 · 3 · 13 - простые множители числа

НОД (32 и 78) = 2 - наибольший общий делитель

НОК (32 и 78) = 2⁵ · 3 · 13 = 1248 - наименьшее общее кратное

Answer 2

To find the greatest common divisor (GCD) and least common multiple (LCM) of two numbers, 32 and 78, we can use the following formulas:

GCD(a, b) = greatest common divisor of a and b LCM(a, b) = least common multiple of a and b

To calculate the GCD of 32 and 78, we can use the Euclidean algorithm.

Step 1: Divide the larger number by the smaller number and keep the remainder. 78 ÷ 32 = 2 remainder 14

Step 2: Now, divide the previous divisor (32) by the remainder (14) and again keep the remainder. 32 ÷ 14 = 2 remainder 4

Step 3: Repeat the process with the previous divisor (14) and the new remainder (4). 14 ÷ 4 = 3 remainder 2

Step 4: Continue with the previous divisor (4) and the new remainder (2). 4 ÷ 2 = 2 remainder 0

Since we have reached a remainder of 0, the last divisor, which is 2, is the GCD of 32 and 78.

GCD(32, 78) = 2

To find the LCM of 32 and 78, we can use the formula:

LCM(a, b) = (a * b) / GCD(a, b)

LCM(32, 78) = (32 * 78) / 2 = 2496 / 2 = 1248

Therefore, the results are: GCD(32, 78) = 2 LCM(32, 78) = 1248