Solution: Find LCM of 5 and 7. Since they are coprime, LCM is $ 5 \times 7 = 35 $. \boxed{35}
["Understanding How to Find the LCM of 5 and 7: A Simple Solution", "When faced with the question “What is the Least Common Multiple (LCM) of 5 and 7?”, many students and learners seek a clear, accurate explanation. The good news is that 5 and 7 are coprime numbers, meaning they share no common factors other than 1. This fundamental property makes calculating their LCM straightforward and efficient.", "### What Does LCM Mean?", "The Least Common Multiple (LCM) of two numbers is the smallest positive number that is evenly divisible by both numbers. For example, multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40… and multiples of 7 are 7, 14, 21, 28, 35, 42… The first number appearing in both sequences is 35.", "### Why Are 5 and 7 Coprime?", "Coprime numbers have a greatest common divisor (GCD) of 1. Since 5 and 7 are both prime numbers and distinct, their GCD is 1. This relationship simplifies the LCM calculation dramatically.", "### The Easy Formula for Coprime Numbers", "For any two coprime integers a and b, the LCM is simply:", "$$\n\mathrm{LCM}(a, b) = a \ imes b\n$$", "Applying this principle:", "$$\n\mathrm{LCM}(5, 7) = 5 \ imes 7 = 35\n$$", "### Real-World Applications of LCM", "Understanding how to compute LCMs helps in solving problems across mathematics, scheduling, and practical scenarios like aligning events that repeat at different intervals. For example, if two buses arrive every 5 and 7 minutes, respectively, they’ll both arrive together every 35 minutes—thanks to their LCM being 35.", "### Final Answer", "The LCM of 5 and 7 is:", "$$\n\boxed{35}\n$$", "Whether you’re a student tackling math homework or someone exploring number theory basics, recognizing that coprime numbers simplify LCM calculations is both elegant and efficient. Next time you ask, “What is the LCM of 5 and 7?”, you’ll confidently reason it’s 35.", "---", "Keywords: LCM 5 and 7, find LCM, LCM of coprime numbers, LCM calculation, math explanation, coprime numbers, 5 and 7 LCM, LCM formula, math tutorial."]
