uestion 3 [Multiples and Factors] Three numbers are given below. Use prime factorisation to determine the HCF and LCM.

To find the HCF and LCM using prime factorization, start by breaking each number down into its prime factors. For example, let's say the numbers are 12, 18, and 30. - 12 = 2² × 3¹ - 18 = 2¹ × 3² - 30 = 2¹ × 3¹ × 5¹ Now, for the HCF, take the lowest power of each prime factor present in all three numbers. So, HCF = 2¹ × 3¹ = 6. For the LCM, take the highest power of each prime factor present in at least one of the numbers. Thus, LCM = 2² × 3² × 5¹ = 180. Voila! You've found both the HCF and LCM! Keep practicing with different numbers to master this skill! Foundations of prime factorization can be traced back to ancient Greeks, particularly Euclid, who introduced systematic ways to find the greatest common divisor. His contributions laid the groundwork for number theory, and today, the methods developed during his time continue to be essential in various branches of mathematics, influencing everything from cryptography to algorithm design. In real-world applications, the concepts of HCF and LCM play a vital role in resource allocation and time management. For instance, in organizing events or scheduling classes, finding the LCM can help determine the optimal timing for recurring activities. Meanwhile, HCF often comes into play in simplifying shared resources, whether it's splitting a pizza evenly among friends or calculating the best way to distribute supplies in a project for efficiency.