MCQ
Mark $(\checkmark)$ against the correct answer in the following: The smallest number which when diminished by $3$ is divisible by $14, 28, 36$ and $45$, is:
- A$1257$
- B$1260$
- C$1263$
- ✓None of these.
✓
Answer
Correct option: D.
None of these.
The smallest number that is exactly divisible by $14, 28, 36$ and $45$ will be their $\text{LCM.}$
So, the required number will be the $\text{LCM}$ plus $3.$
$\begin{array}{c|c}2&11,28,36,45\\\hline2&11,14,18,45\\\hline3&11,7,9,45\\\hline3&11,7,3,15\\\hline5&11,7,1,5\\\hline7&11,7,1,1\\\hline11&11,1,1,1\\\hline&1,1,1,1\end{array}$
$\text{LCM}$ of the three numbers $ = 2^2\times 3^2\times 5 \times 7 \times 11$
$= 13860$
$\therefore $ Required number $= 13860 + 3 = 13863$
So, the required number will be the $\text{LCM}$ plus $3.$
$\begin{array}{c|c}2&11,28,36,45\\\hline2&11,14,18,45\\\hline3&11,7,9,45\\\hline3&11,7,3,15\\\hline5&11,7,1,5\\\hline7&11,7,1,1\\\hline11&11,1,1,1\\\hline&1,1,1,1\end{array}$
$\text{LCM}$ of the three numbers $ = 2^2\times 3^2\times 5 \times 7 \times 11$
$= 13860$
$\therefore $ Required number $= 13860 + 3 = 13863$
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