Question

1)НОД(114,300) 2)НОД(161,350) 3)НОД(108,360) 4)НОД(203,560) 1)НОК(32,48) 2)НОК(100,180) 3)НОК(27,36) 4)НОК(50,297

Answer 1

НОД(114;300)=2×3=6
114=2×3×19
300=3×5×5×2×2
НОД(161;350)=7
161=7×23
350=5×7×2×5
НОД(108;360)=2×2×3×3=36
108=2×3×2×3×3
360=2×3×3×2×2×5
НОД(203;560)=7
203=7×29
560=2×2×7×5×2×2
НОК(32;48)=2×2×2×2×2×3=96
32=2×2×2×2×2
48=3×2×2×2×2
НОК(100;180)=2×3×3×2×5×5=900
100=2×5×5×2
180=2×3×3×2×5
НОК(27;36)=3×3×3×2×2=108
27=3×3×3
36=2×3×2×3
НОК(50;297)=5×5×2×3×3×3×11=14850
50=5×5×2
297=3×3×3×11

Answer 2

To find the greatest common divisor (НОД) and the least common multiple (НОК) of the given numbers, you can use the following formulas and steps:

1. НОД(114, 300):

To find the greatest common divisor, you can use the Euclidean algorithm: Step 1: Divide the larger number by the smaller number and find the remainder. 300 ÷ 114 = 2 with a remainder of 72.

Step 2: Replace the larger number with the smaller number and the smaller number with the remainder from the previous step. 114 ÷ 72 = 1 with a remainder of 42.

Step 3: Repeat the process until you get a remainder of 0. 72 ÷ 42 = 1 with a remainder of 30. 42 ÷ 30 = 1 with a remainder of 12. 30 ÷ 12 = 2 with a remainder of 6. 12 ÷ 6 = 2 with a remainder of 0.

The last nonzero remainder is 6, so the greatest common divisor (НОД) of 114 and 300 is 6.

2. НОД(161, 350):

Using the Euclidean algorithm: 350 ÷ 161 = 2 with a remainder of 28. 161 ÷ 28 = 5 with a remainder of 21. 28 ÷ 21 = 1 with a remainder of 7. 21 ÷ 7 = 3 with a remainder of 0.

The last nonzero remainder is 7, so the greatest common divisor (НОД) of 161 and 350 is 7.

3. НОД(108, 360):

Using the Euclidean algorithm: 360 ÷ 108 = 3 with a remainder of 36. 108 ÷ 36 = 3 with a remainder of 0.

The last nonzero remainder is 36, so the greatest common divisor (НОД) of 108 and 360 is 36.

4. НОД(203, 560):

Using the Euclidean algorithm: 560 ÷ 203 = 2 with a remainder of 154. 203 ÷ 154 = 1 with a remainder of 49. 154 ÷ 49 = 3 with a remainder of 7. 49 ÷ 7 = 7 with a remainder of 0.

The last nonzero remainder is 7, so the greatest common divisor (НОД) of 203 and 560 is 7.

1. НОК(32, 48):

To find the least common multiple, you can use the formula: НОК(a, b) = (a * b) / НОД(a, b)

НОД(32, 48) = 16 (You can calculate this using the Euclidean algorithm as shown in the first example.) НОК(32, 48) = (32 * 48) / 16 = 96.

2. НОК(100, 180):

НОД(100, 180) = 20 (You can calculate this using the Euclidean algorithm as shown in the second example.) НОК(100, 180) = (100 * 180) / 20 = 900.

3. НОК(27, 36):

НОД(27, 36) = 9 (You can calculate this using the Euclidean algorithm.) НОК(27, 36) = (27 * 36) / 9 = 108.

4. НОК(50, 297):

НОД(50, 297) = 1 (You can calculate this using the Euclidean algorithm.) НОК(50, 297) = (50 * 297) / 1 = 14850.

So, the results are:

1. НОД(114, 300) = 6

2. НОД(161, 350) = 7

3. НОД(108, 360) = 36

4. НОД(203, 560) = 7

5. НОК(32, 48) = 96

6. НОК(100, 180) = 900

7. НОК(27, 36) = 108

8. НОК(50, 297) = 14850