Question: A museum curator is cataloging early computing devices and notes that the number of components in a mechanical computer from 1850 is a three-digit number divisible by both 12 and 15. What is the smallest such number that ends in 0?

Sun, 03 May 2026 17:13:25 +0000

The Smallest Three-Digit Number Over 100 Ending in 0, Divisible by Both 12 and 15 When a museum curator is cataloging early computing devices, identifying historical computing components often involves studying the mechanical components used in 19th-century machines. A particular mechanical computer from 1850 features a three-digit number of parts described as divisible by both 12 and 15 — and crucially, the number ends in 0. What is the smallest such number? To find this number, we begin by analyzing the divisibility requirements. ### Step 1: LCM of 12 and 15
Since the number must be divisible by both 12 and 15, it must be divisible by their least common multiple (LCM).
Prime factorizations:
- 12 = 2² × 3
- 15 = 3 × 5
LCM = 2² × 3 × 5 = 60