Question

НОД(210 135) и НОК(16 36)

Answer 1

210 | 2                                          135 | 3

105 | 3                                          45 | 3

35 | 5                                            15 | 3

7 | 7                                               5 | 5

1                                                    1

210 = 2 · 3 · 5 · 7                          135 = 3³ · 5

НОД (210 ; 135) = 3 · 5 = 15 - наибольший общий делитель

210 : 15 = 14

135 : 15 = 9

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

16 | 2                                              36 | 2

8 | 2                                                18 | 2

4 | 2                                                9 | 3

2 | 2                                                3 | 3

1                                                      1

16 = 2⁴                                            36 = 2² · 3²

НОК (16; 36) = 2⁴ · 3² = 144 - наименьшее общее кратное

144 : 16 = 9

144 : 36 = 4

Answer 2

Ответ:

1. 15.

2. 144.

..............

Answer 3

To find the greatest common divisor (GCD) of 210 and 135, you can use the Euclidean algorithm. The Euclidean algorithm involves repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder becomes zero. The last non-zero remainder is the GCD.

Let's apply the Euclidean algorithm:

Step 1: Dividing 210 by 135, we get a quotient of 1 and a remainder of 75.

Step 2: Dividing 135 by 75, we get a quotient of 1 and a remainder of 60.

Step 3: Dividing 75 by 60, we get a quotient of 1 and a remainder of 15.

Step 4: Dividing 60 by 15, we get a quotient of 4 and a remainder of 0.

Since we obtained a remainder of 0, we stop the algorithm. The last non-zero remainder was 15. Therefore, the greatest common divisor (GCD) of 210 and 135 is 15.

To find the least common multiple (LCM) of 16 and 36, you can use the formula:

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

First, let's calculate the GCD of 16 and 36 using the Euclidean algorithm:

Step 1: Dividing 36 by 16, we get a quotient of 2 and a remainder of 4.

Step 2: Dividing 16 by 4, we get a quotient of 4 and a remainder of 0.

Since we obtained a remainder of 0, we stop the algorithm. The last non-zero remainder was 4. Therefore, the greatest common divisor (GCD) of 16 and 36 is 4.

Now, we can calculate the LCM using the formula:

LCM(16, 36) = (16 * 36) / GCD(16, 36) = (16 * 36) / 4 = 576 / 4 = 144

Therefore, the least common multiple (LCM) of 16 and 36 is 144.