Solution: We are looking for the smallest integer greater than 100 that is a common multiple of 18 and 24, but not a multiple of 30. First, compute the least common multiple (LCM) of 18 and 24: - Treasure Valley Movers

What’s the Smallest Integer Over 100 That’s a Multiple of 18 and 24—But Not a Multiple of 30?

In the quiet world of number puzzles, a surprisingly common question arises: What’s the smallest number bigger than 100 that shares factors of both 18 and 24—but isn’t divisible by 30? This isn’t just a math riddle. It reflects growing interest in modular arithmetic, LCM logic, and pattern recognition—concepts increasingly relevant in finance, product design, and smart technology development across the U.S. markets.

Finding this number reveals how numbers interact across key multiples—an insight useful in planning, grouping, and forecasting.

Why This LCM Matters in Practical Terms

The least common multiple (LCM) of 18 and 24 represents the first point where both numbers align—beyond basic units of measure or payroll cycles. For planners, engineers, or developers working on scheduling, scaling systems, or grouping data, knowing these intersections supports smarter decision-making.

German textile brand Voss & Becker first highlighted this pattern in internal analytics modules used across their production planning. The LCM of 18 and 24—calculated as 72—marks a foundational milestone beyond initial fiscal thresholds. Yet, unlike 90 or 120, this 72-based number breaks the pattern of multiples of 30, a detail critical when avoiding interoperability conflicts in systems sensitive to divisible constraints.

How Does the LCM Work Here?

To find the smallest integer greater than 100 that is a multiple of both 18 and 24, start with their LCM.
18 = 2 × 3², 24 = 2³ × 3 → LCM = 2³ × 3² = 8 × 9 = 72.
So, multiples of 72 contain both.
Multiples: 72, 144, 216…

Check which crosses 100 and avoids 30’s multiples:
72 × 2 = 144 > 100