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144 cartons of Coke Cans and 90 cartons of Pepsi Cans are to be stacked in a Canteen. If each stack is of the same height and is to contain cartons of the same drink, what would be the greatest number of cartons each stack would have?

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answer is C.

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Detailed Solution

Given,
The number of cartoons of coke cans = 144
The number of cartoons from Pepsi cans = 90
As per Euclid’s Division Lemma, if there are two positive integers a and b, then there exist unique q and r such that they satisfy the condition:

a = bq + r

where

0 \leq r < b

Calculation of HCF of 144 and 90 by using Euclid’s algorithm is as follows,

144 = 90 \times 1 + 54

\Rightarrow 90 = 54 \times 1 + 36

\Rightarrow 54 = 36 \times 1 + 18

\Rightarrow 36 = 18 \times 2 + 0

\Rightarrow HCF (144, 90) = 18

Therefore, the greatest number of cartons each stack would have been 18.
Hence, option 3 is correct.

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