Вопрос:

Найдите НОК чисел: 1) 11 и 12; 2) 16 и 18; 3) 125 и 75; 4) 190 и 920; 5) 24, 68 и 162; 6) 588 и 252; 7) 675 и 995; 8) 924 и 396; 9) 995 и 825

Ответ:

Решение:

  1. 11 и 12:

    НОК(11, 12) = 11 × 12 = 132

  2. 16 и 18:

    16 = 24

    18 = 2 × 32

    НОК(16, 18) = 24 × 32 = 16 × 9 = 144

  3. 125 и 75:

    125 = 53

    75 = 3 × 52

    НОК(125, 75) = 3 × 53 = 3 × 125 = 375

  4. 190 и 920:

    190 = 2 × 5 × 19

    920 = 23 × 5 × 23

    НОК(190, 920) = 23 × 5 × 19 × 23 = 8 × 5 × 19 × 23 = 17480

  5. 24, 68 и 162:

    24 = 23 × 3

    68 = 22 × 17

    162 = 2 × 34

    НОК(24, 68, 162) = 23 × 34 × 17 = 8 × 81 × 17 = 11016

  6. 588 и 252:

    588 = 22 × 3 × 72

    252 = 22 × 32 × 7

    НОК(588, 252) = 22 × 32 × 72 = 4 × 9 × 49 = 1764

  7. 675 и 995:

    675 = 33 × 52

    995 = 5 × 199

    НОК(675, 995) = 33 × 52 × 199 = 27 × 25 × 199 = 134325

  8. 924 и 396:

    924 = 22 × 3 × 7 × 11

    396 = 22 × 32 × 11

    НОК(924, 396) = 22 × 32 × 7 × 11 = 4 × 9 × 7 × 11 = 2772

  9. 995 и 825:

    995 = 5 × 199

    825 = 3 × 52 × 11

    НОК(995, 825) = 3 × 52 × 11 × 199 = 3 × 25 × 11 × 199 = 164025

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