Identify the odd number: Among 39, 69, 57, and 117, exactly one is a multiple of 19. Choose that number.

Introduction / Context:
Targeted-divisor checks (like 19) often produce a unique outlier in a small set.

Given Data / Assumptions:

• Candidates: 39, 69, 57, 117.
• We test divisibility by 19.

Concept / Approach:
Compare with nearby multiples: 19, 38, 57, 76, 95, 114, 133, …

Step-by-Step Solution:

Verification / Alternative check:
Dividing each by 19: only 57/19 = 3 is an integer.

Why Other Options Are Wrong:
They are not multiples of 19; 117 is close (114 is 19 * 6) but not equal.

Common Pitfalls:
Choosing numbers near a multiple of 19 (e.g., 117) instead of exact multiples.

Final Answer:
57 is the only multiple of 19 and hence the odd number.