Question

144 red cartons and 90 blue cartons are to be stacked in a canteen. If each stack is of the same height and is to contain cartons of the same colour, then the greatest number of cartons in each stack would be

• A. 8
• B. 5
• C. 18
• D. 36

Answer 1

The correct option is C 18

Here,
the greatest number of cartons in each stack = HCF (144,90)
Applying Euclid's division lemma
$144=90\times 1+54$
Here, Remainder $\ne$ 0, so apply again
$90=54\times 1+36$
Apply Lemma again, as Remainder $\ne$ 0
$54=36\times 1+18$
Apply Lemma again, as Remainder $\ne$ 0
$36=18\times 2+0$
Now, remainder is 0
So, required answer is 18
Hence, correct option is c.