A sustainability director is evaluating annual waste reduction targets. What is the smallest three-digit number that is divisible by both 8 and 9, and whose digits sum to a multiple of 9? - Sterling Industries
The Smallest Three-Digit Number That Meets Waste Target Criteria—And Why It Matters
The Smallest Three-Digit Number That Meets Waste Target Criteria—And Why It Matters
When sustainability leaders review annual waste reduction goals, they face precise yet subtle challenges. One often-overlooked requirement is identifying a three-digit number that satisfies strict divisibility and digital criteria—particularly useful in reporting, budgeting, and performance tracking. For example: What is the smallest three-digit number divisible by both 8 and 9, with a digit sum that’s also a multiple of 9?
This question reflects a growing emphasis on measurable, data-driven environmental commitments across US-based organizations. As waste reduction becomes more systematized, leaders need clear benchmarks—not just abstract targets but quantifiable milestones. This number, often overlooked in casual contexts, serves as a tangible example of how precision supports accountability in sustainability planning.
Understanding the Context
Why Is This Number Relevant to Waste Management Strategy?
Today’s US sustainability directors manage complex reporting cycles, aligning corporate or municipal waste data with evolving regulatory and stakeholder expectations. Divisibility by both 8 and 9 introduces a unique mathematical constraint, making it a useful tool for filtering datasets, creating reporting ranges, or simplifying financial planning. Paired with a digit sum that’s a multiple of 9, it reinforces internal consistency—ensuring numbers align across operations, from material tracking to carbon accounting.
In the broader trend toward standardized ESG and waste diversion metrics, such clear numerical benchmarks enhance clarity and reduce ambiguity in progress tracking. This makes them valuable not only for internal reporting but also when communicating performance in public dashboards or investor communications.
Key Insights
What Is the Smallest Three-Digit Number That Fits the Criteria?
To find the answer, we begin with the least common multiple (LCM) of 8 and 9, which is 72. We then identify the smallest three-digit multiple of 72:
72 × 2 = 144
144 is a valid three-digit number.
Next, verify the digit sum: 1 + 4 + 4 = 9 — a multiple of 9, satisfying both divisibility
