Question

What is the smallest number which when increased by $5$ is completely divisible by $8$, $11$ and $24$?

• A. $264$
• B. $259$
• C. $269$
• D. $238$

Answer 1

Answer: (B)

$259$

$\Rightarrow$ $8=2\times 4=2\times 2\times 2=2^3$

$\Rightarrow$ $11=1\times 11=11$

$\Rightarrow$ $24=2\times 12=2\times 2\times 6=2\times 2\times 2\times 3=2^3\times 3$

$\Rightarrow$ Take the union of all of those to get the smallest possible number = $2^3\times 11\times 3=264$

$\therefore$ The smallest number which is increased by 5 = $264-5=259$