Notăm:
[tex]a = 12 \cdot m, \ \ b = 12 \cdot n, \ \ (m,n)\neq1, \ \ m,n \in \Bbb{N^{\ast}}\\[/tex]
Avem formula:
[tex]\boldsymbol{a \cdot b = (a,b) \cdot [a,b]} \iff 12m \cdot 12n = 12 \cdot 360\\[/tex]
[tex]\implies \boldsymbol{m \cdot n = 30}[/tex]
a<b ⇒ m<n
[tex]30 = 1 \cdot 30 = 3 \cdot 10 = 5 \cdot 6\\[/tex]
[tex]m=1, \ n=30 \implies a=12\cdot1=1, \ \ b=12\cdot30=360\\[/tex]
[tex]m=3, \ n=10 \implies a=12\cdot3=36, \ \ b=12\cdot10=120\\[/tex]
[tex]m=5, \ n=6 \implies a=12\cdot5=60, \ \ b=12\cdot6=72\\[/tex]
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Notăm:
[tex]a = 12 \cdot m, \ \ b = 12 \cdot n, \ \ (m,n)\neq1, \ \ m,n \in \Bbb{N^{\ast}}\\[/tex]
Avem formula:
[tex]\boldsymbol{a \cdot b = (a,b) \cdot [a,b]} \iff 12m \cdot 12n = 12 \cdot 360\\[/tex]
[tex]\implies \boldsymbol{m \cdot n = 30}[/tex]
a<b ⇒ m<n
[tex]30 = 1 \cdot 30 = 3 \cdot 10 = 5 \cdot 6\\[/tex]
[tex]m=1, \ n=30 \implies a=12\cdot1=1, \ \ b=12\cdot30=360\\[/tex]
[tex]m=3, \ n=10 \implies a=12\cdot3=36, \ \ b=12\cdot10=120\\[/tex]
[tex]m=5, \ n=6 \implies a=12\cdot5=60, \ \ b=12\cdot6=72\\[/tex]