Question

The smallest number which when increased by $17$ is exactly divisible by both $520$ and $468$ is :

• A. $4697$
• B. $4656$
• C. $4663$
• D. $4680$

Answer 1

The correct option is C

$4663$

Solution:

Step 1: Calculate the LCM of $520\mathrm{and}468$ :

$$\begin{gathered} 520=2\times 2\times 2\times 5\times 13 \\ 468=2\times 2\times 3\times 3\times 13 \\ \therefore \mathbf{LCM}\left(520,468\right)=2\times 2\times 2\times 3\times 3\times 5\times 13 \\ =4680 \end{gathered}$$

Step 2: Calculate the required number:

To obtain the smallest number which when increased by $17$ is exactly divisible by both $520\mathrm{and}468$, we have to subtract $17$ from the LCM.

Therefore,

$$\begin{gathered} \mathbf{LCM}\left(520,468\right)-17=4680-17 \\ =\mathbf{4663} \end{gathered}$$

Final answer: Hence, option C is the correct answer.