Question

Two different machines are used to manufacture a product. The $1^{st}$ machine makes the top part, $14$ in each batch, and the $2^{nd}$ machine makes the bottom part, $16$ in each batch. Each top part is assembled with the bottom part and released to the sales department.

Find the minimum number of batches needs to be produced by the $2^{nd}$ machine such that no unassembled parts are left.

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is B $7$

The $1^{st}$ machine produces $14$ top parts in a batch.
The $2^{nd}$ machine produces $16$ bottom parts in a batch.

It is given that no unassembled parts are left.
$\therefore$ For minimum number of batches from $2^{nd}$ machine, the total number of assembled products should be minimum.
$\Rightarrow$ Number of assembled products is a common multiple of $14$ and $16.$
$\Rightarrow$ The minimum number of assembled products is the least common multiple of $14$ and $16.$

Using ladder diagram,
LCM $=2^4\times 7=112$

$\therefore$ The minimum number of assembled products is $112.$

Minimum number of batches required from $2^{nd}$ machine
$=\frac{\text{Number of assembled products}}{\text{Number of parts per batch}}$
$=\frac{112}{16}$
$=7$