Q:

What is the LCM of 120 and 148?

Accepted Solution

A:
Solution: The LCM of 120 and 148 is 4440MethodsHow to find the LCM of 120 and 148 using Prime FactorizationOne way to find the LCM of 120 and 148 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 120?What are the Factors of 148?Here is the prime factorization of 120:23×31×512^3 × 3^1 × 5^123×31×51And this is the prime factorization of 148:22×3712^2 × 37^122×371When 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: 2, 3, 5, 3723×31×51×371=44402^3 × 3^1 × 5^1 × 37^1 = 444023×31×51×371=4440Through this we see that the LCM of 120 and 148 is 4440.How to Find the LCM of 120 and 148 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 120 and 148 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, 120 and 148:What are the Multiples of 120?What are the Multiples of 148?Let’s take a look at the first 10 multiples for each of these numbers, 120 and 148:First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200First 10 Multiples of 148: 148, 296, 444, 592, 740, 888, 1036, 1184, 1332, 1480You 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 120 and 148 are 4440, 8880, 13320. Because 4440 is the smallest, it is the least common multiple.The LCM of 120 and 148 is 4440.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 20 and 103?What is the LCM of 101 and 47?What is the LCM of 51 and 137?What is the LCM of 146 and 115?What is the LCM of 89 and 63?