Find the greatest number of six digits which on being divided by 6, 7, 8, 9 and 10 leaves 4, 5, 6, 7 and 8 as remainder respectively.

Question

Find the greatest number of six digits which on being divided by 6, 7, 8, 9c, and 10 leaves 4, 5, 6, 7, and 8 as remainder respectively.

(a) 997920

(b) 997918

(c) 997922

(d) 997930

Answer 1

Correct option : (b) 997918

The common difference between the divisors and the respective remainders 

\(= (6 - 4) = 7 - 5 = 8 - 6\)

\(=9-7=10-8=2\).

LCM of 6, 7, 8, 9 and 10 = 2520.

\(\therefore\) Required number is 2520k - 2.

Greatest number of six digits is 999999.

Now,

 

\(\therefore\) k = 396

Hence, required number is \(2520\times 396 -2\)

\(=997920-2 =997918.\)