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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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