Question: A drone’s camera can capture images every 6 seconds, and a second drone captures images every 10 seconds. After how many seconds will both drones capture an image at the same time? - High Altitude Science
Title: When Do Drones Capture Images Together? Finding the Common Timing Interval
Title: When Do Drones Capture Images Together? Finding the Common Timing Interval
When using two drones equipped with cameras for synchronized data collection, you may wonder: after how many seconds will both drones capture images simultaneously? In a practical scenario, one drone captures an image every 6 seconds, while the second takes a picture every 10 seconds. But how can you determine exactly when their capture cycles align? This beginner-friendly guide explains the concept of least common multiples (LCM) and shows you step-by-step how to calculate the precise moment both drones capture images at the same time.
Understanding the Context
Understanding the Problem
Drone A captures an image every 6 seconds: at times 6, 12, 18, 24, …
Drone B captures an image every 10 seconds: at times 10, 20, 30, 40, …
We want to know: after how many seconds will both drones capture images simultaneously for the first time?
This happens at the least common multiple (LCM) of their capture intervals — 6 and 10.
Key Insights
What Is the Least Common Multiple (LCM)?
The LCM of two numbers is the smallest number that is a multiple of both. It represents the first time both events (in this case, image captures) coincide.
Step 1: Prime Factorization
Break down each number into prime factors:
- 6 = 2 × 3
- 10 = 2 × 5
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Step 2: Identify Each Prime Factor
Take the highest power of each prime that appears:
- Prime factor 2: appears as 2¹
- Prime factor 3: appears as 3¹
- Prime factor 5: appears as 5¹
Step 3: Multiply the Highest Powers Together
LCM = 2¹ × 3¹ × 5¹ = 2 × 3 × 5 = 30
Conclusion: The First Simultaneous Image Capture
Both drones will capture images together for the first time exactly 30 seconds after startup. They will again capture simultaneously every 30 seconds thereafter.
