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Wait — $ \textlcm(7,8,9) $: - AssociationVoting

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Question: Two research teams are analyzing plant species across different continents. One team analyzes data from 48 regions, and the other from 72 regions. What is the largest number of regions that could be in each group if they want to divide both datasets into groups of equal size without any regions left out?

📌 Solution: To divide both 48 and 72 regions into equal-sized groups with no regions left out, we must find the greatest common divisor (GCD) of 48 and 72.

📌 We use prime factorization:

📌 = 2^4 \times 3,\quad 72 = 2^3 \times 3^2

📌 The GCD is obtained by taking the minimum exponent for each common prime:

📌 \text{GCD}(48, 72) = 2^3 \times 3 = 8 \times 3 = 24

📌 Thus, the largest number of regions that can be in each group is

📌 Question: A science journalist is organizing a chart showing the number of flower species observed in 360 different samples. If each chart column represents a number of samples and the number of columns must be a multiple of both 6 and 10, what is the smallest number of samples per column possible?

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