Đáp án:

`301` học sinh

Giải thích các bước giải:

Giải:

Gọi số học sinh đó là `a` , `a < 400`

Ta có:

`a` chia cho `2,3,4,5,6` đều dư `1`

`=> a - 1` chia hết cho `2,3,4,5,6`

`=> a - 1 ∈ BC(2,3,4,5,6)`

Ta có:

`BCNN(2,3,4,5,6) = 3*4*5 = 60`

`=> a - 1 ∈ {0;60;120;180;240;300;360;420}`

`=> a - 1 ∈ {60;120;180;240;300;360}`

`=> a ∈ {61;121;181;241;301;361}`

Mà `a \vdots 7`

`=> a = 301`

Vậy số học sinh khối đó là `301` bạn

Gọi số học sinh là $a$ ($a$ $∈$ N*; $a$ $<$ $400)$

Ta có:

$a$ $-$ $1$ $\vdots$ $2$

$a$ $-$ $1$ $\vdots$ $3$

$a$ $-$ $1$ $\vdots$ $4$

$a$ $-$ $1$ $\vdots$ $5$

$a$ $-$ $1$ $\vdots$ $6$

$a$ $\vdots$ $7$

⇒ $a$ $-$ $1$ $∈$ $BC(2,3,4,5,6)$

Ta có:

$2$ $=$ $2$

$3$ $=$ $3$

$4$ $=$ $2^2$

$5$ $=$ $5$

$6$ $=$ $2$ $.$ $3$

⇒ $BCNN(2,3,4,5,6)$ $=$ $2^2$ $.$ $3$ $.$ $5$ $=$ $60$

Vậy $BC(2,3,4,5,6)$ $=$ {$0$; $60$; $120$; $180$; $240$; $300$; ...}

⇒ $a$ $-$ $1$ $∈$ {$0$; $60$; $120$; $180$; $240$; $300$; ...}

⇒ $a$ $∈$ {$1$; $61$; $121$; $181$; $241$; $301$; ...}

Vì $a$ $<$ $400$ nên $a$ $∈$ {$1$; $61$; $121$; $181$; $241$; $301$; $361$}

Ta có: $a$ $\vdots$ $7$

Vì: $1$ $:$ $7$ $=$ $0$ $($dư $1)$

$61$ $:$ $7$ $=$ $8$ $($dư $5)$

$121$ $:$ $7$ $=$ $17$ $($dư $3)$

$181$ $:$ $7$ $=$ $25$ $($dư $6)$

$241$ $:$ $7$ $=$ $34$ $($dư $3)$

$301$ $:$ $7$ $=$ $43$

$361$ $:$ $7$ $=$ $51$ $($dư $4)$

⇒ $a$ $=$ $301$

Vậy có $301$ học sinh