Răspuns:
36
Explicație pas cu pas:
12 | 2. 12 = 2² × 3. 18 | 3
6 | 2. 18= 2× 3² 6 | 3
3 | 3. 2 | 2
1 / 1 /
c.m.m.m.c = 2²×3²=( 2×3 )²=6²=36
[tex]\mathrm{cmmmc}(a,b) = \dfrac{|a\cdot b|}{\mathrm{cmmdc}(a,b)}\\\\[/tex]
Folosesc algoritmul lui Euclid pentru a afla cmmdc.
[tex]\\\mathrm{cmmdc(12,18)} = \mathrm{cmmdc}\Big((12,18-12) = (12,6) = (12-6,6)\Big) =\\ \\ =\mathrm{cmmdc}(6,6) = 6\\ \\ \Rightarrow \mathrm{cmmmc}(12,18)=\dfrac{|12\cdot 18|}{6} = \boxed{36}[/tex]
