There are 21 mango trees, 42 apple trees, and 56 orange trees to be planted in rows. Each row must contain the same number of trees and only one variety per row. What is the minimum total number of rows required?

Introduction / Context:
This is a greatest common divisor (GCD) application. To minimize the number of rows, we maximize how many trees go in each row, which must be the same for all varieties. That maximum per-row count is the GCD of the three totals.

Given Data / Assumptions:

• Mango trees = 21
• Apple trees = 42
• Orange trees = 56
• Each row: same number of trees; single variety only

Concept / Approach:
If x is the number of trees per row, then x must divide 21, 42, and 56. The largest such x is gcd(21, 42, 56). The minimum number of rows then equals 21/x + 42/x + 56/x.

Step-by-Step Solution:
gcd(21, 42) = 21; gcd(21, 56) = 7 ⇒ gcd(21, 42, 56) = 7.Trees per row = 7.Rows for each variety: 21/7 = 3 (mango), 42/7 = 6 (apple), 56/7 = 8 (orange).Total minimum rows = 3 + 6 + 8 = 17.

Verification / Alternative check:
Any larger per-row count would not divide at least one total; any smaller per-row count increases rows, so 17 is minimal.

Why Other Options Are Wrong:
15, 18, and 20 correspond to using a non-maximal divisor; 3 counts only one variety’s rows, not the total.

Common Pitfalls:
Using LCM instead of GCD; mixing varieties in a single row; or summing counts incorrectly.

Final Answer:
17