Solution: The LCM of 11 and 111 is 1221MethodsHow to find the LCM of 11 and 111 using Prime FactorizationOne way to find the LCM of 11 and 111 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:What are the Factors of 11?What are the Factors of 111?Here is the prime factorization of 11:11111^1111And this is the prime factorization of 111:31×3713^1 × 37^131×371When 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: 11, 3, 3731×111×371=12213^1 × 11^1 × 37^1 = 122131×111×371=1221Through this we see that the LCM of 11 and 111 is 1221.How to Find the LCM of 11 and 111 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 11 and 111 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number. Let’s take a look at the multiples for each of these numbers, 11 and 111:What are the Multiples of 11?What are the Multiples of 111?Let’s take a look at the first 10 multiples for each of these numbers, 11 and 111:First 10 Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 11 and 111 are 1221, 2442, 3663. Because 1221 is the smallest, it is the least common multiple.The LCM of 11 and 111 is 1221.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 105 and 10?What is the LCM of 97 and 128?What is the LCM of 142 and 28?What is the LCM of 20 and 102?What is the LCM of 31 and 54?