The least number which leaves no remainder when divided by 4, 6, 8 and 9, and leaves a remainder of 7 when divided by 13, is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 72
A number divisible by 4, 6, 8 and 9 is a multiple of their LCM. The multiples are tried in order until one leaves remainder 7 on division by 13.
\(4=2^{2}\), \(6=2\times3\), \(8=2^{3}\), \(9=3^{2}\)
LCM \(=2^{3}\times3^{2}=72\)
First multiple: 72, and \(72=13\times5+7\), remainder 7
The least such number is 72.