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Question

Two different machines are used to manufacture a product. The first machine makes the top part, 14 in each batch, and the second 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 product needs to be produced such that no unassembled parts are left.


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Solution

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

It is given that no unassembled parts are left.
Number of assembled products is a common multiple of 14 and 16.
The minimum number of assembled products is the least common multiple of 14 and 16.

Using ladder diagram,
LCM =24×7=112

Required number of assembled products is 112.

For this, first machine have to make 8 batches and second machine have to make 7 batches.

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