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.

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?

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

Continue Reading

rac{8!}{3! \cdot 2! \cdot 3!} = rac{40320}{6 \cdot 2 \cdot 6} = rac{40320}{72} = 560
Now compute $ \left( rac{1}{3}
ight)^8 = rac{1}{6561} $

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Final Thoughts

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.