Solution: The LCM of 42 and 125 is 5250MethodsHow to find the LCM of 42 and 125 using Prime FactorizationOne way to find the LCM of 42 and 125 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 42?What are the Factors of 125?Here is the prime factorization of 42:21×31×712^1 × 3^1 × 7^121×31×71And this is the prime factorization of 125:535^353When 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: 2, 3, 7, 521×31×53×71=52502^1 × 3^1 × 5^3 × 7^1 = 525021×31×53×71=5250Through this we see that the LCM of 42 and 125 is 5250.How to Find the LCM of 42 and 125 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 42 and 125 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, 42 and 125:What are the Multiples of 42?What are the Multiples of 125?Let’s take a look at the first 10 multiples for each of these numbers, 42 and 125:First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420First 10 Multiples of 125: 125, 250, 375, 500, 625, 750, 875, 1000, 1125, 1250You 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 42 and 125 are 5250, 10500, 15750. Because 5250 is the smallest, it is the least common multiple.The LCM of 42 and 125 is 5250.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 121 and 27?What is the LCM of 15 and 135?What is the LCM of 72 and 57?What is the LCM of 6 and 81?What is the LCM of 4 and 129?