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

Answer: Option C

LCM of (4, 5, 6, 7, 8) = 4 × 5 × 6 × 7 = 840
⇒ Required number = 840k + 2, which is divisible by 13
$$\begin{array}{rl}& \text{For }\frac{840k+2}{13},\left(\text{remainder}=0\right)\\ & \text{Remainder}=\frac{8k+2}{13}\end{array}$$
Put k = 3
Then, remainder = 0
For least multiple value of k is minimum
⇒ at k = 3 we get 840k + 2
= 840 × 3 + 2
= 2520 + 2
= 2522