Question

While arranging oranges in heaps of$24,32and48$, a fruit vendor notices that $8$ oranges are always left. What is the smallest number of oranges he has?

• A. $96$
• B. $104$
• C. $88$
• D. $124$

Answer 1

The correct option is A

$96$

A fruit vendor arranging oranges in heaps of$24,32and48$

Number of oranges that always left = $8$

Smallest number of oranges he has = LCM of $24,32and48$

Step 1:

Write factors of $24,32and48$

$$\begin{gathered} 24=2\times 2\times 2\times 3 \\ =2^3\times 3 \end{gathered}$$

$$\begin{gathered} 32=2\times 2\times 2\times 2\times 2 \\ =2^5 \end{gathered}$$

$$\begin{gathered} 48=2\times 2\times 2\times 2\times 3 \\ =2^4\times 3 \end{gathered}$$

LCM is $2^5\times 3$

$=96$