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[a,b]=240
a×b=2880
Determimați numerele naturale nenule a şi b , cu a < b


Răspuns :

(a,b)x[a,b]=axb => (a,b)x240=2880 =>
(a,b)=2880:240=12
(a,b)=12 => (a,b)€{(1,12),(2,6),(3,4)}
cu placere
(a;b)[a;b]=ab
(a;b) x 240=2880
(a;b)=12
a=12m
b=12n, (m;n)=1
a x b=12^2 x m x n=2880
mn=20
m=1, n=20, a=12, b=240
m=4, m=5, a=48, b=60
m=5, n=4 nu
m=20, n=1 nu