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 $1683$

LCM of $5,6,7$ and $8=840$.
Hence the number can be written in the form $(840k+3)$ which is divisible by $9.$
If $k=1$, number $=(840\times 1)+3=843$ which is not divisible by $9.$
If $k=2$, number $=(840\times 2)+3=1683$ which is divisible by $9.$
Hence, $1683$ is the least number which when divided by $5,6,7$ and $8$ leaves a remainder $3$, but when divided by $9$ leaves no remainder.