Найти НОК и НОД чисел: а) 180 и 120 б) 280 и 360 в) 48 и 72

Решение:

а) 180 = 2 × 2 × 3 × 3 × 5;

120 = 2 × 2 × 2 × 3 × 5;

НОК (180; 120) = 2 × 2 × 3 × 3 × 5 × 2 = 360;

НОД (180; 120) = 2 × 2 × 3 × 5 = 60;

б) 280 = 2 × 2 × 2 × 5 × 7;

360 = 2 × 2 × 2 × 3 × 3 × 5;

НОК (280; 360) = 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2 520;

НОД (280; 360) = 2 × 2 × 2 × 5 = 40;

в) 48 = 2 × 2 × 2 × 2 × 3;

72 = 2 × 2 × 2 × 3 × 3;

НОК (48; 72) = 2 × 2 × 2 × 3 × 3 × 2 = 144;

НОД (48; 72) = 2 × 2 × 2 × 3 = 24.