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. 2523
• C. 3363
• D. 1683

Answer 1

The correct option is D 1683

Let the least number be $x$,

$x=$ multiple of L.C.M. $(5,6,7,8)+3[\therefore x\text{given remainder 3 when divided by}5,6,7,8]$

$=$ multiple of $840+3$

$=840k+3$

$k=0$ $x=3$ Remainder with $9=8$

$k=1$ $x=843$ Remainder with $9=6$

$k=2$ $x=1683$ Remainder with $9=0[9\times 187=1683]$

Hence $x=1683$