Question: What is the smallest three-digit number representing the population threshold for a community, divisible by both 12 and 18, ensuring equitable resource distribution? - Parker Core Knowledge
The Smallest Three-Digit Number Over 100 That’s Divisible by Both 12 and 18 – Ensuring Equitable Resource Distribution
The Smallest Three-Digit Number Over 100 That’s Divisible by Both 12 and 18 – Ensuring Equitable Resource Distribution
When designing sustainable communities, one crucial threshold often dictates resource allocation: the smallest three-digit population number that is evenly divisible by both 12 and 18. This number isn’t arbitrary—it reflects a balance where infrastructure, services, and equity can be efficiently and fairly distributed among residents.
What Makes a Population Threshold Significant?
Understanding the Context
Communities thrive when their population falls within specific ranges—for example, ensuring schools, hospitals, and public utilities operate optimally without overextension. The key mathematical threshold is the least common multiple (LCM) of key numbers governing resource compatibility. Here, the threshold must be divisible by both 12 and 18, guaranteeing smooth integration across planning cycles governed by these multiples.
Finding the Smallest Three-Digit Number Divisible by 12 and 18
To find the smallest three-digit number divisible by both 12 and 18, we first compute their least common multiple.
- Prime factorization:
- 12 = 2² × 3
- 18 = 2 × 3²
- 12 = 2² × 3
- LCM takes the highest powers: 2² × 3² = 4 × 9 = 36
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Key Insights
So, any community size divisible by 36 qualifies. The smallest three-digit number divisible by 36 is found by dividing 100 by 36:
100 ÷ 36 ≈ 2.78 → next whole number is 3
36 × 3 = 108
✅ 108 is the smallest three-digit number divisible by both 12 and 18.
Why 108 Matters for Equitable Resource Distribution
Choosing 108 as a population threshold offers several key advantages:
- Divisibility: Easy to divide communities into balanced units (e.g., 12 sectors of 9 residents, or 18 clusters of 6).
- Efficiency: Public services like transit routes, schools, and emergency response systems can be deployed in fractions that align with the number’s factors.
- Equity: The number allows fair averaging—per capita resource allocation remains consistent, supporting just distribution without favoring larger subgroups.
- Scalability within constraints: While 108 is the smallest threshold under 200, larger communities centered on similar multiples (e.g., 216, 324) maintain the same equitable principles.
Real-World Implications
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Urban planners and policy makers use thresholds like 108 to define manageable community scales where:
- Infrastructure investment supports evenly distributed needs.
- Budget planning aligns with predictable population units.
- Equity metrics—like per capita healthcare or education access—remain stable and just.
Conclusion
The smallest three-digit number representing a viable community population threshold divisible by both 12 and 18 is 108. This number supports equitable resource distribution by enabling balanced planning, efficient service delivery, and fair access across all residents. Whether designing new towns or allocating regional budgets, recognizing 108 as a foundational metric fosters sustainable, just communities built on sound mathematical principles.
Keywords: smallest three-digit number divisible by 12 and 18, population threshold community planning, equitable resource distribution, least common multiple 12 18, 108 community size, fair population scaling, public service allocation, urban sustainability metrics.
