Răspuns:
a) 24 şi 56 -» c.m.m.m.c
24 | 2
12 | 2
6 | 2
3 | 3
1 |
56 | 2
28 | 2
14 | 2
7 | 7
1 |
24 = 2³ × 3
56 = 2³ × 7
[24, 35] = 2³ × 3 × 7
[24, 35] = 8 × 3 × 7
[24, 35] = 24 × 7
[24, 35] = 168
b) 5, 15, 30 şi 45 -» c.m.m.m.c
5 | 5
1 |
15 | 3
5 | 5
1 |
30 | 2
15 | 3
5 | 5
1 |
45 | 3
15 | 3
5 | 5
1 |
5 = 5
15 = 3 × 5
30 = 2 × 3 × 5
45 = 3² × 5
[5, 15, 30, 45] = 2 × 3² × 5
[5, 15, 30, 45] = 2 × 9 × 5
[5, 15, 30, 45] = 18 × 5
[5, 15, 30, 45] = 90
c) 450 şi 1.300 -» c.m.m.m.c
450 | 2
225 | 3
75 | 3
25 | 5
5 | 5
1 |
1.300 | 2
650 | 2
325 | 5
65 | 5
13 | 13
1 |
450 = 2 × 3² × 5²
1.300 = 2² × 5² × 13
[450, 1.300] = 2² × 3² × 5² × 13
[450, 1.300] = 4 × 9 × 25 × 13
[450, 1.300] = 36 × 325
[450, 1.300] = 11.700
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