HCF and LCM of 55 ans 210

To find the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of 55 and 210, we first break both numbers down into their prime factors. For 55, the prime factorization is 5 × 11. For 210, the prime factorization is 2 × 3 × 5 × 7. Now, the HCF is determined by taking the common factors, which in this case is 5. Therefore, the HCF of 55 and 210 is 5. For the LCM, we take the highest power of all prime factors from both numbers. This gives us: 2^1 × 3^1 × 5^1 × 7^1 × 11^1 = 2310. So, the LCM of 55 and 210 is 2310. Did you know that the concept of HCF and LCM has been around for centuries? Ancient mathematicians, such as those in Babylon and China, utilized these ideas to solve problems related to sharing resources and trade. They needed to figure out how to divide goods evenly or find the smallest common size of items, leading to the development of these important mathematical concepts. Understanding how to calculate HCF and LCM plays a significant role in fields like engineering, computer science, and even music! For example, when engineers design systems or structures that need to function together, knowing the best way to combine sizes and intervals can be crucial. Similarly, musicians use LCM to find common rhythms and beats when playing in ensembles, ensuring everyone is in sync!