Question: What is the smallest three-digit number divisible by the number of letters in "climate" and "modeling"?
["Smallest Three-Digit Number Divisible by the Number of Letters in "Climate" and "Modeling": A Step-by-Step Breakdown", "When tackling math puzzles, understanding word-based clues is key—especially when numbers are tied to letter counts. One intriguing question asks: What is the smallest three-digit number divisible by the number of letters in "climate" and "modeling"? Let’s break down how to solve this problem efficiently, including the letter counts, calculations, and final answer.", "---", "### Understanding the Question", "The core of the problem involves two components:\n1. The number of letters in the word climate\n2. The number of letters in the word modeling", "We’re looking for the smallest three-digit number—that is, from 100 to 999—divisible by both these letter counts. For a number to be divisible by two values, it must be divisible by their least common multiple (LCM).", "---", "### Step 1: Count Letters in Each Word", "- "climate" has 7 letters\n- "modeling" has 8 letters", "So, we need the smallest three-digit number divisible by both 7 and 8.", "---", "### Step 2: Compute the Least Common Multiple (LCM)", "To find a number divisible by both 7 and 8, calculate the least common multiple:", "- 7 is prime\n- 8 = 2³", "Since 7 and 8 share no common prime factors, their LCM is simply their product:\n[\n\ ext{LCM}(7, 8) = 7 \ imes 8 = 56\n]", "Thus, any number divisible by both 7 and 8 must be divisible by 56.", "---", "### Step 3: Find the Smallest Three-Digit Multiple of 56", "Now, identify the smallest number ≥ 100 divisible by 56.", "Divide 100 by 56 to find the starting point:\n[\n100 \div 56 \approx 1.786\n]", "Rounding up gives 2, so the smallest multiple is:\n[\n56 \ imes 2 = 112\n]", "---", "### Step 4: Verify the Result", "- 112 is a three-digit number ✔\n- Is it divisible by 7?\n [\n 112 \div 7 = 16 \quad \ ext{(no remainder, divisible)}\n ]\n- Is it divisible by 8?\n [\n 112 \div 8 = 14 \quad \ ext{(no remainder, divisible)}\n ]", "Both conditions are satisfied.", "---", "### Final Answer", "The smallest three-digit number divisible by the number of letters in "climate" (7) and "modeling" (8) is 112.", "---", "### Why This Matters: SEO & Clarity", "This SEO-friendly article connects word analysis, number theory, and problem-solving logic with clear, structured steps. Using keywords like “smallest three-digit number divisible by 7 and 8”, “LCM of 7 and 8”, and “how to find LCM” boosts searchability while educating readers. The step-by-step approach improves readability and encourages engagement—key for SEO success.", "If you’re solving similar puzzles, always start by counting relevant letters, compute the LCM, and test multiples—simple and reliable!"]
