144 cartons of Coke Cans and 90 cartons of Pepsi Cans are to be stacked in a Canteen.
Question:

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?

Solution:

Given that 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 contains cartons of the same drink We need to find the greatest number of cartons, each stack would have

Given that

Number of cartons of coke cans = 144

Number of cartons of Pepsi cans = 90.

Therefore, the greatest number of cartons in one stack = H.C.F. of 144 and 90.

By applying Euclid’s division lemma

$144=90 \times 1+54$

$90=54 \times 1+36$

$54=36 \times 1+18$

$36=18 \times 2+0$

H.C.F. $=18$

Hence, the greatest number cartons in one stack 18

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