Question

Вычислите НОД и НОК чисел: 237 и 215; 1998 и 111; 25 и 27.

Answer 1

1) 237 = 1·3·79;   215 = 1·5·43.

НОД(237, 215) = 1

НОК(237, 215) = 3·79·5·43 = 237·215 = 237·(200+10+5) = 47 400 + 2 370 + 1 185 = 50 955

2) 1998 = 2·9·37 = 2·3²·37;   111 = 3·37.

НОД(1998, 111) = 3·37 = 111

НОК(1998, 111) = 2·3²·37 = 1998

3) 25 = 1·5²;   27 = 1·3³

НОД(25; 27) = 1

НОК(25, 27) = 5²·3³ = 25·27 = 25·(20+7) = 500+175 = 675