What is the smallest five-digit number which, when divided by 7, 11 and 21, leaves a remainder 3 in each case?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10167
A number that leaves the same remainder 3 when divided by 7, 11 and 21 is 3 more than a number that all three divide without a remainder, that is, 3 more than a multiple of their LCM.
21 \(=3\times7\), so LCM of 7, 11 and 21 \(=3\times7\times11=231\)
\(10000\div231\) gives quotient 43, and \(43\times231=9933\) has only four digits
The next multiple, \(44\times231=10164\), is the smallest five-digit multiple of 231
Required number \(=10164+3=10167\)