Timber lengths 42 m, 49 m, and 63 m are to be cut into planks of equal length with no waste. What is the greatest possible length of each plank?

Introduction / Context:
To maximize the uniform plank length that exactly divides all given lengths, we take the greatest common divisor (GCD) of the three lengths. This ensures no waste and equal-size planks.

Given Data / Assumptions:

• Lengths: 42 m, 49 m, 63 m
• Planks must have equal maximum possible length

Concept / Approach:
The largest length that divides all three numbers evenly is gcd(42, 49, 63). Use prime factorization or Euclidean algorithm to compute it.

Step-by-Step Solution:
gcd(42, 49) = 7 (since 42 = 2 * 3 * 7, 49 = 7^2)gcd(7, 63) = 7 (since 63 = 3^2 * 7)Therefore, the greatest plank length = 7 m.

Verification / Alternative check:
42/7 = 6, 49/7 = 7, 63/7 = 9; all integral.

Why Other Options Are Wrong:
14 m, 21 m, 42 m, and 63 m do not divide all three lengths without remainder.

Common Pitfalls:
Mistaking LCM for GCD or not checking divisibility across all lengths.

Final Answer:
7 m