Question

Đã trả lời bởi chuyên gia

Answer 1

a) Ta có: 30 = 2 . 3 . 5; 45 = 3² . 5

BCNN(30, 45) = 2. 3² . 5 = 90

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

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: $x \in B C (34, 85) = B (170) = \{0; 170; 340; 510; 680; 850; 1020; ...\}$

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

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

BCNN(12, 21, 28) = 2² . 3 . 7 = 84

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

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

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

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

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

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

e, Vì _{$x ⋮ 39; x ⋮ 65; x ⋮ 91$} nên $x \in B C (39, 65, 91)$

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

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

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

Mà 400 < x < 2600 → x = 1365

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Answer 2