Question

The least number which when divided by $5,6,7$ and $8$ leaves a remainder $3$, but when divided by $9$ leaves no remainder, is.

• A. $1677$
• B. $1683$
• C. $2523$
• D. $3363$

Answer 1

The correct option is B $1683$

R.E.F image

$\to$ First of all taking LCM of $5,6,7,8$

$\to$ The LCM will be $840$.

$\to$ So we need a number i.e., $840\times x+3$.

$\to$ we will put least value of x which is

divisible by $9$.

$\therefore k=2$

$\therefore$ Required number$=840\times 2+3=1683$.