Question: What is the smallest three-digit number divisible by 11 and 13?
["What is the Smallest Three-Digit Number divisible by 11 and 13?", "When exploring numbers divisible by both 11 and 13, many people wonder: what is the smallest three-digit number that satisfies this condition? The answer isn’t just a random number—it’s a key example of finding the least common multiple (LCM) within a specific numerical range. In this article, we’ll explore the mathematical logic behind the problem and reveal the smallest three-digit number divisible by 11 and 13.", "### Understanding LCM and Three-Digit Numbers", "The LCM of two numbers is the smallest positive integer that both numbers divide without leaving a remainder. Since 11 and 13 are both prime, their LCM is simply their product:", "[\n\ ext{LCM}(11, 13) = 11 \ imes 13 = 143\n]", "So, 143 is the smallest number divisible by both 11 and 13. But is it a three-digit number? Yes—143 is between 100 and 999, confirming it qualifies as a three-digit number.", "### Why 143 is the Answer", "Since 143 is the LCM of 11 and 13, it is the least such number. All subsequent multiples—286, 429, 572, and so on—are larger three- or four-digit numbers. Therefore, 143 is the smallest three-digit number divisible by both 11 and 13.", "### How to Find It Easily", "Instead of checking every three-digit number, we can rely on the LCM:", "- Begin with the smallest three-digit multiple of 11, which is 110, and keep adding 11.\n- Alternatively, begin with 143, the direct LCM, and verify it’s a three-digit number (which it is).", "Using ideas like these simplifies solving similar problems involving divisibility, LCM, and range constraints.", "### Real-Life Use and Interest", "Finding such numbers isn’t just academic—it’s useful in mathematics, coding, cryptography, and even scheduling. Knowing the smallest three-digit multiple helps with efficient computation, especially in algorithms requiring deterministic ranges.", "### Summary", "- The least common multiple of 11 and 13 is 143.\n- 143 is the smallest three-digit number divisible by both.\n- Checking multiples or using LCM avoids unnecessary computation.", "So, the answer to “What is the smallest three-digit number divisible by 11 and 13?” is 143—a neat intersection of prime numbers and divisibility rules.", "---", "Keywords: smallest three-digit number divisible by 11 and 13, LCM of 11 and 13, smallest three-digit multiple of 143, how to find LCM in three-digit range, number theory basics, practical math problem.", "Meta Description: Discover the smallest three-digit number divisible by both 11 and 13—learn how the LCM of prime numbers produces 143 and why it’s the answer."]
