Question

The least multiple of $13,$ which on dividing by $4,5,6,7$ and $8$ leaves remainder $2$ in each case, is

• A. $2520$
• B. $842$
• C. $2522$
• D. $840$

Answer 1

Answer: (C)

$2522$

LCM of 4,5,6,7 & 8 = 840

Let require number be 840k+2 which is

multiple of 13.

Let say k = 1. No : $842÷13\Rightarrow$ Remainder 10

k = 2 No : $1682÷13\Rightarrow$ Remainder 5

k = 3 No : $2522÷13\Rightarrow$ Remainder is 0

that mean 2522 is the least number we Required.