Find the least number which when divided by 12, leaves a remainder of 7, when divided by 15, leaves a remainder of 10 and when divided by 16, leaves a remainder of 11.

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A number when divided by 7,11 and 13 (the prime factor of 1001) successively leave the remainder 6,10 and 12 respectively. Find the remainder if the number is divided by 1001.

The correct option is C 1000L.C.M. of 7, 11 and 13 =1001So, the required no. can be 1001 - 1 = 1000or 2002 - 1 = 2001 and so on∴ The remainder when it is divided by 1001 is always = 1000

A number when divided by $7, 11$ and $13$ (the prime factor of $1001$ ) successively leave the remainder $6, 10$ and $12$ respectively. Find the remainder if the number is divided by $1001$ .

The correct option is C $1000$
L.C.M. of 7, 11 and 13 $=$ 1001
So, the required no. can be 1001 - 1 $=$ 1000
or 2002 - 1 $=$ 2001 and so on
$∴$ The remainder when it is divided by 1001 is always $=$ 1000