As your math tutor, I'm here to guide you through this problem! To find the LCM of 61 and 113, one effective method is comparing their prime factorizations. Start by breaking each number down into its prime factors. Follow these steps to determine the prime factorization of each number:
Here is the prime factorization of 61:
And this is the prime factorization of 113:
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 61, 113
Through this we see that the LCM of 61 and 113 is 6893.