$\text{Ta có: 2a = 3b = 5c}$
$\text{BCNN( 2; 3; 5) = 30}$
$\text{⇔ $\dfrac{2a}{30}$ = $\dfrac{3b}{30}$ = $\dfrac{5c}{30}$ }$
$\text{⇒ $\dfrac{a}{15}$ = $\dfrac{b}{10}$ = $\dfrac{c}{6}$ }$
$\text{⇒ $\dfrac{a}{15}$ = $\dfrac{b}{10}$ = $\dfrac{2c}{12}$ }$
$\text{Áp dụng tính chất dãy tỉ số bằng nhau ta có:}$
$\text{$\dfrac{a}{15}$ = $\dfrac{b}{10}$ = $\dfrac{2c}{12}$ = $\dfrac{a - b + 2c}{15 - 10 + 12}$ = $\dfrac{34}{17}$ = 2}$
$\text{Do đó:}$
$\text{$\dfrac{a}{15}$ = 2 ⇒ a= 30}$
$\text{$\dfrac{b}{10}$ = 2 ⇒ b = 20}$
$\text{$\dfrac{2c}{12}$ = 2 ⇔ $\dfrac{c}{6}$ = 2 ⇒ c =12}$
$\text{Vậy a = 30}$
$b = 20$
$c = 12$
