Question: What is the smallest three-digit number divisible by 14 and 21, representing the minimal batch size for synchronized seismic sensor calibration? - Redraw
What is the Smallest Three-Digit Number Divisible by 14 and 21? Understanding the Minimal Batch Size for Seismic Sensor Calibration
What is the Smallest Three-Digit Number Divisible by 14 and 21? Understanding the Minimal Batch Size for Seismic Sensor Calibration
When calibrating seismic sensors—critical tools used in earthquake monitoring, environmental research, and geological surveying—ensuring precision and consistency requires standardized testing batches. A key question arises: What is the smallest three-digit number divisible by both 14 and 21? This calculation isn’t just academic; it directly represents the minimal batch size for synchronized calibration, enabling accurate data collection across multiple sensor arrays.
The Mathematical Foundation: LCM of 14 and 21
Understanding the Context
To determine the smallest three-digit number divisible by both 14 and 21, we must first compute the Least Common Multiple (LCM) of these two numbers.
- Prime factorization:
- 14 = 2 × 7
- 21 = 3 × 7
- 14 = 2 × 7
The LCM takes the highest power of each prime factor:
LCM(14, 21) = 2 × 3 × 7 = 42
Thus, any number divisible by both 14 and 21 must be a multiple of 42.
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Key Insights
Finding the Smallest Three-Digit Multiple of 42
We now seek the smallest three-digit multiple of 42. Three-digit numbers range from 100 to 999.
Divide the smallest three-digit number, 100, by 42:
100 ÷ 42 ≈ 2.38
The next whole number is 3, so:
42 × 3 = 126
Since 126 is a three-digit number and divisible by both 14 and 21:
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- 126 ÷ 14 = 9 → divisible
- 126 ÷ 21 = 6 → divisible
126 meets all criteria.
Why 126 Matters in Seismic Sensor Calibration
In practical terms, a batch size of 126 sensors ensures full synchronization during calibration—a crucial step when aligning sensitive devices that detect minute ground movements. Using the LCM means each sensor completes a calibration cycle in step, minimizing timing discrepancies and maximizing data reliability.
For research teams, environmental monitoring stations, or disaster preparedness agencies, understanding this minimal batch size optimizes resource use without sacrificing measurement accuracy.
Summary
- Smallest three-digit number divisible by both 14 and 21 is 126.
- This value is the LCM of 14 and 21.
- Represents the minimal synchronized batch size for seismic sensor calibration.
- Enables efficient, precise alignment critical for earthquake monitoring and geoscience research.
Leveraging mathematical principles like LCM ensures not only technical accuracy but also operational efficiency in real-world sensor deployment. Whether deploying new seismic arrays or standardizing maintenance protocols, knowing key numerical thresholds like 126 empowers smarter scientific workflows.
Keywords: smallest three-digit number divisible by 14 and 21, LCM 14 and 21, seismic sensor calibration, minimal batch size, earthquake monitoring, sensor synchronization, seismic array calibration
