Question

LKD(216; 148) un LKD(165; 255).

Answer 1

216 | 2                                     148 | 2

108 | 2                                     74 | 2

54 | 2                                      37 | 37

27 | 3                                       1

9 | 3                                         148 = 2² · 37

3 | 3

1

216 = 2³ · 3³

НОД (216 и 148) = 2² = 4 - наибольший общий делитель

216 : 4 = 54                         148 : 4 = 37

НОК (216 и 148) = 2³ · 3³ · 37 = 7992 - наименьшее общее кратное

7992 : 216 = 37                   7992 : 148 = 54

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165 | 3                                  255 | 3

55 | 5                                   85 | 5

11 | 11                                     17 | 17

1                                            1

165 = 3 · 5 · 11                      255 = 3 · 5 · 17

НОД (165 и 255) = 3 · 5 = 15 - наибольший общий делитель

165 : 15 = 11                         255 : 15 = 17

НОК (165 и 255) = 3 · 5 · 11 · 17 = 2805 - наименьшее общее кратное

2805 : 165 = 17                   2805 : 255 = 11

Answer 2

To find the greatest common divisor (GCD) of two numbers, we can use the Euclidean algorithm. Let's apply this algorithm to find the GCD of 216 and 148:

1. Divide 216 by 148: 216 = 1 * 148 + 68.
2. Divide 148 by 68: 148 = 2 * 68 + 12.
3. Divide 68 by 12: 68 = 5 * 12 + 8.
4. Divide 12 by 8: 12 = 1 * 8 + 4.
5. Divide 8 by 4: 8 = 2 * 4 + 0.

The remainder becomes zero at this point, which means that the GCD of 216 and 148 is the last non-zero remainder, which is 4. Therefore, the GCD of 216 and 148 is 4.

Now, let's find the GCD of 165 and 255:

1. Divide 255 by 165: 255 = 1 * 165 + 90.
2. Divide 165 by 90: 165 = 1 * 90 + 75.
3. Divide 90 by 75: 90 = 1 * 75 + 15.
4. Divide 75 by 15: 75 = 5 * 15 + 0.

Again, the remainder becomes zero, indicating that the GCD of 165 and 255 is the last non-zero remainder, which is 15. Therefore, the GCD of 165 and 255 is 15.

So, the GCD of 216 and 148 is 4, while the GCD of 165 and 255 is 15.