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Therefore, the Smallest Positive Integer Divisible by Both 7 and 5 is 35 When exploring the fundamentals of mathematics, one question often arises: What is the smallest positive integer divisible by both 7 and 5? This query is not only a gateway to understanding multiples but also strengthens foundational number theory skills. For learners, students, and math enthusiasts alike, solving this problem illuminates the concept of least common multiples (LCM)—a key concept in mathematics and real-world applications. ### What Does It Mean to Be Divisible by Both 7 and 5?
A number divisible by both 7 and 5 must be a multiple of both. In other words, it should leave no remainder when divided by either 7 or 5. While any multiple of 7 and 5 individually technically satisfies this, we seek the smallest such positive integer—this is precisely the definition of the least common multiple (LCM). ### Finding the Least Common Multiple (LCM)
To calculate the LCM of two numbers, one effective method is prime factorization.