A science administrator must distribute $1.8 million in research grants among three climate research projects. Project X requires funding every 3 years, Project Y every 4 years, and Project Z every 6 years. To align disbursements, the administrator wants to invest in full cycles of each project. What is the minimum number of years after which all three projects will simultaneously require funding again, assuming perfect alignment at year zero?

Wed, 06 May 2026 12:08:44 +0000

**Why A Science Administrator Must Distribute $1.8 Million in Climate Research Grants—Syncing Full Cycles of Funding**
With growing urgency around climate resilience, how research funding aligns with project timelines shapes progress. Project X receives $600,000 every 3 years, Project Y every 4 years, and Project Z every 6 years—all starting in year zero. Understanding when these cycles converge reveals critical planning opportunities for administrators. In an era of intensified climate investments, synchronizing disbursements ensures stable progression without gaps. **What’s the Minimum Year All Projects Align Again?**
The key lies in identifying the Least Common Multiple (LCM) of 3, 4, and 6. This mathematical foundation determines when all funding cycles restart together. Calculating step-by-step, LCM(3, 4, 6) = 12. Therefore, after 12 years, Projects X, Y, and Z will simultaneously request funding again—marking the next full alignment since their launch. **Why This Shift Matters in Climate Research Planning**
Climate science funding demands long-term stability. By recognizing full funding cycles align every 12 years, administrators can better forecast resource availability, coordinate milestones, and sustain scientific momentum. This insight helps avoid delays and supports strategic budgeting in federal and institutional grant portfolios. **Common Questions About Funding Synchronization**
**H3: How Are Funding Cycles Determined?**
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