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: Option C

Solution(By Examveda Team)

LCM of (4, 5, 6, 7, 8) = 4 × 5 × 6 × 7 = 840
⇒ Required number = 840k + 2, which is divisible by 13
$$\eqalign{ & {\text{For }}\frac{{840k + 2}}{{13}},\,\,\left( {{\text{remainder}} = 0} \right) \cr & {\text{Remainder}} = \frac{{8k + 2}}{{13}} \cr} $$
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