Завдання:
Знайди найбільший спільний дільник і найменше спільне кратне чисел:
1) 14 і 3;
2) 36 і 30;
3) 18 і 6;
4) 26 і 39.
Розв'язок:
1) 14 і 3:
14 = 2 ⋅ 7;
3 = 3;
НСД (14; 3) = 1;
НСК (14; 3) = 14 ⋅ 3 = 42;
2) 36 і 30:
36 = 2 ⋅ 2 ⋅ 3 ⋅ 3;
30 = 2 ⋅ 3 ⋅ 5;
НСД (36; 30) = 2 ⋅ 3 = 6;
НСК (36; 30) = 2 ⋅ 3 ⋅ 2 ⋅ 3 ⋅ 5 = 180;
3) 18 і 6:
18 = 2 ⋅ 3 ⋅ 3;
6 = 2 ⋅ 3;
НСД (18; 6) = 2 ⋅ 3 = 6;
НСК (18; 6) = 2 ⋅ 3 ⋅ 3 = 18;
4) 26 і 39:
26 = 2 ⋅ 13;
39 = 3 ⋅ 13;
НСД (26; 39) = 13;
НСК (26; 39) = 2 ⋅ 3 ⋅ 13 = 78.