A Party Store sells large plates in packs of 12 and small plates in packs of 8. If you would like to have an equal number of both, what is the least amount of large plates you will have to buy?

1 Answer
Shwetank Mauria
Apr 15, 2016

#24#

Explanation:

As one can get large plates only in multiples of #12#, and one can buy #{1,2,3,4,5,6,7,8,...}# packs and one will purchasing #{12,24,36,48,60,72,84,96,....}# large plates.

As one can get small plates only in multiples of #8#, and one can buy #{1,2,3,4,5,6,7,8,9,10,11,12,...}# packs and one will purchasing #{8,16,24,32,40,48,56,64,72,80,88,96,....}# small plates.

But as one has to purchase equal number of plates, one can buy only #{24,48,72,96,...}# plates and hence least amount of large plates one will have to buy is #24#.

Note this is equivalent to finding Lease Common Multiple (LCM) and hence one could have directly arrived at the answer by calculating LCM of #8# and #12#, which is #24#.

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