What is the smallest four-digit number that is divisible by both 8 and 9?

Tue, 21 Apr 2026 09:34:08 +0000

**What is the smallest four-digit number that is divisible by both 8 and 9?** What is the smallest four-digit number that is divisible by both 8 and 9?
It’s a simple question—but behind the digits lies a pattern many people are exploring as computational details intersect with digital awareness. This number isn’t just a milestone in number theory; it’s quietly gaining traction in discussions around efficiency, precision, and systems optimization across the U.S. market. What’s the significance behind finding such a number? As digital platforms and financial systems grow more complex, identifying efficient building blocks—like numbers divisible by multiple criteria—helps streamline algorithms, coding challenges, and even financial benchmarks. The smallest four-digit number meeting these divisibility requirements, 1008, marks a foundational starting point in a system that values both mathematical integrity and practical utility. To unpack how 1008 satisfies both conditions, it starts with the least common multiple (LCM) of 8 and 9. Since 8 = 2³ and 9 = 3²—sharing no common factors—their LCM is 8 × 9 = 72. The smallest four-digit multiple of 72 is found by calculating: 1000 ÷ 72 ≈ 13.89, so the next integer is 14. Multiplying 72 × 14 gives 1008. This step-by-step calculation reveals both precision and efficiency in problem-solving.