Question

Find the largest four-digits number which when divided by 4, 7 and 13 leaves a remainder of 3 in each case.

Answer 1

Largest 4 digit number is 9999
To find the largest 4 digit number divisible by 4, 7 and 13, we find the LCM of 4, 7 and 13 first.
LCM(4, 7, 13) = $4\times 7\times 13$ = 364
Now, to we divide 9999 by 364 and subtract the remainder from 9999 to get the number completely divisible by 4, 7 and 13.

$9999-171=9828$
Because the number leaves the remainder 3, so we add 3 to 9828.
Therefore, 9828 + 3 = 9831 is the required number.