Знайди найбільший спільний дільник і найменше спільне кратне чисел:
1) 48 і 56;
2) 12 і 7;
3) 22 і 33;
4) 9 і 36.
Розв'язок:
1) 48 і 56:
48 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3;
56 = 2 ⋅ 2 ⋅ 2 ⋅ 7;
НСД (48; 56) = 2 ⋅ 2 ⋅ 2 = 8;
НСК (48; 56) = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 7 = 168;
2) 12 і 7:
12 = 2 ⋅ 2 ⋅ 3;
7 = 7 ⋅ 1;
НСД (12; 7) = 1;
НСК (12; 7) = 12 ⋅ 7 = 84;
3) 22 і 33:
22 = 2 ⋅ 11;
33 = 3 ⋅ 11;
НСД (22; 33) = 11;
НСК (22; 33) = 11 ⋅ 2 ⋅ 3 = 66;
4) 9 і 36:
9 = 3 ⋅ 3;
36 = 2 ⋅ 2 ⋅ 3 ⋅ 3;
НСД (9; 36) = 3 ⋅ 3 = 9;
НСК (9; 36) = 3 ⋅ 3 ⋅ 2 ⋅ 2 = 36.