Question

НОД(168,231) НОК(75,45)

Answer 1

168 = 2 • 2 • 2 • 3 • 7
231 = 3 • 7 • 11
НОД (168; 231) = 3 • 7 = 21
НОК (168, 231) = 3 • 7 • 11 • 2 • 2 • 2 = 1848

Answer 2

To find the greatest common divisor (НОД) of 168 and 231, and the least common multiple (НОК) of 75 and 45, you can use the following calculations:

1. Greatest Common Divisor (НОД) of 168 and 231: You can use the Euclidean algorithm to find the greatest common divisor.

Step 1: Divide 231 by 168. 231 ÷ 168 = 1 remainder 63

Step 2: Now divide 168 by 63. 168 ÷ 63 = 2 remainder 42

Step 3: Divide 63 by 42. 63 ÷ 42 = 1 remainder 21

Step 4: Divide 42 by 21. 42 ÷ 21 = 2 remainder 0

The remainder has become 0, so the greatest common divisor is the last non-zero remainder, which is 21.

So, НОД(168, 231) = 21.

2. Least Common Multiple (НОК) of 75 and 45: To find the least common multiple, you can use the formula:

НОК(a, b) = (a * b) / НОД(a, b)

Here, a = 75 and b = 45.

НОД(75, 45) = 15 (which can be found using the same Euclidean algorithm as above)

Now plug these values into the formula:

НОК(75, 45) = (75 * 45) / 15 = 225

So, НОК(75, 45) = 225.