Đáp án:
Giải thích các bước giải:
Ta có:
$a= 36q+ 34a+ 2= 36q+ 34+ 2= 36q+ 36= 36. (q+ 1)$
$a= 40k+ 38⇒ a+ 2= 40k+ 38+ 2= 40k+ 40= 4. (k+ 1)$
$a= 42m+ 40. a+ 2= 42m+ 40+ 2= 42. m+ 42= 42. (m+ 1)$
$⇒ a+ 2$ $\vdots$ $36, 40, 42$
$⇒ a+ 2∈ BCNN (36, 40, 42)$
$36= 2^3. 3^2$
$40 =2^3. 5$
$42= 2. 3. 7$
$⇒ BCNN (36, 40, 42)= 2^3. 3^2. 5. 7= 2520$
$⇒ a+ 2= 2520$
$⇒ a= 2520- 2$
$⇒ a= 2518$
Vậy số tự nhiên nhỏ nhất là $2518$
ko sai đề!
Gọi số cần tìm là : $a$ ($ a ∈ N*; a nhỏ nhất$)Ta có:$\left\{\begin{matrix}a chia 36 dư 34 & \\ a chia 40 dư 38& \\ a chia 42 dư 40 & \end{matrix}\right.$ $⇒$ $a+2$ $∈$ `BC(36;40;42)`$⇒$ $a+2$ = `BCNNNN(36;40;42)` vì $a$ nhỏ nhất$36 =2^2 . 3^2$$40 = 2^3 . 5$$42 = 2.3.7$$⇒ a+2 = 2^3 . 3^2 . 5 . 7 =2520 ⇔ a = 2518$ Vậy số phải tìm là $2518$
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lm hộ mình cái minh yêu nhiều nha <3
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