During a sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If you want full packs of both and the same number of pencils and crayons, how many of each would you need to buy?

Given: 

Number of colour pencils in a pack  $=$  24

Number of crayons in a pack  $=$  32

To find: Here we have to find the number of packets for each (pencils and crayons) we need to buy to have the same number of pencils and crayons.

Solution:

To find the same number of pencils and crayons we need to find the LCM of 24 and 32.

Now,

Writing the numbers as a product of their prime factors:

Prime factorisation of 24:

• $2\ \times\ 2\ \times\ 2\ \times\ 3\ =\ 2^3\ \times\ 3^1$

Prime factorisation of 32:

• $2\ \times\ 2\ \times\ 2\ \times\ 2\ \times\ 2\ =\ 2^5$

Multiplying the highest power of each prime number:

• $2^5\ \times\ 3^1\ =\ 96$

Thus,

LCM(24, 32)  $=$  96

So,

The number of packs of pencils  $=\ \frac{96}{24}\ =$  4 packs

The number of packs of crayon  $=\ \frac{96}{32}\ =$  3 packs

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Updated on: 10-Oct-2022

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