Question

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 each would you need to buy?

Answer 1

Since, we want equal numbers of crayons and pencils and we have the liberty to buy more thus, we will find LCM. Had the question been to equally distribute the given number of pencils and colours then we would have found the HCF.

To find the required number of pencils and crayons, we need to find the LCM of $24$ and $32$.
Prime factorisation of $24=2\times 2\times 2\times 3$
Prime factorisation of $32=2\times 2\times 2\times 2\times 2$
∴ Required LCM of $24$ and $32=2\times 2\times 2\times 2\times 2\times 3=96$
Thus, number of pencils and crayons needed to be bought is $96$ each.