a: UCLN=30

BCNN=360

b: UCLN=12

BCNN=720

Câu a:

90 = 2.3^2.5; 120 = 2^3.5.3

BCNN(90; 120) = 2^3.3^2.5 = 360

ƯCLN(90 ; 120) = 2.3.5 = 30

a)541 + (218 - x) = 735

(218 - x) = 735 - 541

(218 - x) = 194

x = 218 - 194

x = 24

\(10000-x \times24=541\times16\)

\(10000-x\times24=8656\)

\(x\times24=10000-8656\)

\(x\times24=1344\)

`x=1344:24`

`x=56`

10 000 - X x 24 = 541 x 16

10 000 - X x 24 = 8656

              X x 24 = 10 000 - 8656 

             X  x 24 = 1344

             X           = 1344: 24

              X           = 56 

\(480=2^5.3.5\)

\(288=2^5.3^2\)

\(160=2^5.5\)

\(\text{Ư}CLN=2^5.3=96\)

\(B\left(96\right)=\left\{0;96;192;288;384;...\right\}\)

ƯCLN (480;288;160)

Phân tích ra thừa số nguyên tố, ta có kết quả sau :

480 = 2^5 . 3 . 5

288 = 2^5 . 3^2

160 = 2^5 . 5

Chọn 2

Suy ra UwCLN (480;288;160)=2^5=32

B(32) = {0;32;64;96;128;160;192;...}
 

1)

a) 18 = 2.3²

30 = 2.3.5

ƯCLN(18; 30) = 2.3 = 6

b) 24 = 2³.3

48 = 2⁴.3

ƯCLN(24; 48) = 2³.3 = 24

c) 18 = 2.3²

30 = 2.3.5

15 = 3.5

ƯCLN(18; 30; 15) = 3

d) 24 = 2³.3

48 = 2⁴.3

36 = 2².3²

ƯCLN(24; 48; 36) = 2².3 = 12

2) a) 174 = 18 . 9 + 12

18 = 12 . 1 + 6

12 = 6 . 2

Vậy ƯCLN(174; 18) = 6

b) 124 = 16 . 7 + 12

16 = 12 . 1 + 4

12 = 4 . 3

⇒ ƯCLN(124; 16) = 4

⇒ BCNN(124; 16) = 124 . 16 : 4 = 496

541 + (218 – x) = 735

    218 – x = 735 – 541

    218 - x = 194

    x = 218 – 194

(542 - 541)²⁹³⁸ = 1²⁹³⁸ = 1

(542 + 541)⁰ = 1083⁰ = 1

Vậy : (542  - 541)²⁹³⁸ = (542 + 541)⁰ (đpcm)

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