Tìm các số tự nhiên x, biết:

a) x$\in$BC(30, 45), x < 500;

b) x $\in$BC(34, 85), 500 < x < 1000;

c) x $\in$BC(12, 21, 28), 150 < x < 300;

d)  x $\in$BC(65, 45, 105) và x là số có bốn chữ số;

e) x39; x 65, x 91 và 400 < x < 2600.

a) Ta có: 30 = 2 . 3 . 5; 45 = 3² . 5

BCNN(30, 45) = 2. 3² . 5 = 90

Suy ra: $x\in BC\left(30,45\right)=B\left(90\right)=\left\{0;90;180;270;360;450;540;\mathrm{...}\right\}$

Mà $x<500\Rightarrow x\in \{0;90;180;270;360;450\}$

b) Ta có: 34 = 2 . 17; 85 = 5 . 17

BCNN(34; 85) = 2 . 17 . 5 = 170

Suy ra:$x\in BC\left(34,85\right)=B\left(170\right)=\left\{0;170;340;510;680;850;1020;\mathrm{...}\right\}$

Mà $500<x<1000\Rightarrow x\in \left\{510;680;850\right\}$

c, Ta có: 12 = 2² . 3; 21 = 3 . 7; 28 = 2² . 7

BCNN(12, 21, 28) = 2² . 3 . 7 = 84

Suy ra: $x\in BC\left(12,21,28\right)=B\left(84\right)=\left\{0,84,168,252,336,\mathrm{...}\right\}$

Mà $150<x<300\Rightarrow x\in \left\{168;252\right\}$

d, Ta có: 65 = 5 . 13; 45 = 3² . 5; 105 = 3 . 5 . 7

BCNN(65; 45; 105) = 3² . 5 . 7 . 13 = 4095

Suy ra: $x\in BC\left(65,45,105\right)=B\left(4095\right)=\left\{0;4095;8190;12285;\mathrm{...}\right\}$

Mà x có bốn chữ số $\Rightarrow x\in \left\{4095;8190\right\}$

e, Vì _{$x⋮39;x⋮65;x⋮91$} nên $x\in BC\left(39,65,91\right)$

Ta có: 39 = 3.13; 65 = 5.13; 91 = 7.13

BCNN(39,65,91) = 3.5.7.13 = 1365

Suy ra $x\in BC\left(39,65,91\right)=B\left(1365\right)=\left\{0,1365,2730,\mathrm{...}\right\}$

Mà 400 < x < 2600 → x = 1365