Найдите наименьшее общее кратное чисел:

1) 60; 24; 36;

2) 30; 45; 105;

3) 80; 88; 220;

4) 36; 90; 200;

5) 56; 140; 350;

6) 72; 108; 144;

7) 90; 60; 135;

8) 100; 80; 120;

9) 35; 68; 187.

1) 60; 24; 36

60 = 2*2*3*5 = 2 ² * 3*5

24 = 2*2*2*3 = 2³ * 3

36 = 2*2*3*3 = 2² * 3²

НОК (60; 24; 36) = 2² * 3*5*2*3 = 360

2) 30; 45; 105

30 = 2*3*5

45 = 3*3*5 = 3 ² * 5

105 = 3*5*7

НОК (30; 45; 105) = 3*5*7*2*3 = 630

3) 80; 88; 220

80 = 2*2*2*2*5 = 2 ⁴ * 5

88 = 2*2*2*11 = 2³ * 11

220 = 2*2*5*11 = 2² * 5*11

НОК (80; 88; 220) = 2² * 5*11*2² = 880

4) 36; 90; 200

36 = 2*2*3*3 = 2² * 3²

90 = 2*3*3*5 = 2*3² * 5

200 = 2*2*2*5*5 = 2³ * 5²

НОК (36; 90; 200) = 2³ * 5² * 3² = 1800

5) 56; 140; 350

56 = 2*2*2*7 = 2³ * 7

140 = 2*2*5*7 = 2² * 5*7

350 = 2*5*5*7 = 2*5² * 7

НОК (56; 140; 350) = 2*5² * 7 * 2² = 1400

6) 72; 108; 144

72 = 2*2*2*3*3 = 2³ * 3²

108 = 2*2*3*3*3 = 2² * 3³

144 = 2*2*2*2*3*3 = 2⁴ * 3²

НОК (72; 108; 144) = 2⁴ * 3² * 3 = 432

7) 90; 60; 135

90 = 2*3*3*5 = 2*3² * 5

60 = 2*2*3*5 = 2² * 3*5

135 = 3*3*3*5 = 3³ * 5

НОК (90; 60; 135) = 3³ * 5 * 2² = 540

8) 100; 80; 120

100 = 2*2*5*5 = 2 ² * 5²

80 = 2*2*2*2*5 = 2⁴ * 5

120 = 2*2*2*3*5 = 2³ * 3*5

НОК (100; 80; 120) = 2³ * 3*5 * 5*2 = 1200

9) 35; 68; 187

35 = 5*7

68 = 2*2*17 = 2 ² * 17

187 = 11*17

НОК (35; 68; 187) = 11*17*2 ² * 5*7 = 26180