The smallest positive integer that is evenly divisible by both 17 and 14 is calculated by finding the least common multiple. This value represents the minimum quantity that incorporates both 17 and 14 as factors. Since 17 is a prime number, and 14 is the product of 2 and 7, there are no common factors between 17 and 14 other than 1. Therefore, the least common multiple is obtained by multiplying the two numbers together. Specifically, the product of 17 and 14 is 238. Thus, 238 is the least common multiple.
Understanding the smallest common multiple has practical applications in various fields. In mathematics, it aids in simplifying fractions and solving problems related to ratios and proportions. In real-world scenarios, it can be utilized to solve scheduling problems or when aligning events that occur at different intervals. While the concept may seem abstract, its utility extends beyond theoretical calculations, providing a basis for solving problems in diverse settings.
