Question
A company wants to pack 144 small boxes, 216 medium
boxes, and 288 large boxes into cartons such that each carton contains the same number of boxes of each size. What is the minimum number of cartons required?Solution
To minimize the number of cartons, each carton must contain the greatest number of boxes of each size that can divide 144, 216, and 288 evenly. Maximum number of boxes in each carton = HCF(144, 216, 288) = 24. Number of cartons for small boxes = 144 / 24 = 6. Number of cartons for medium boxes = 216 / 24 = 9. Number of cartons for large boxes = 288 / 24 = 12. Total number of cartons = 6 + 9 + 12 = 27. Correct Option: c) 27
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