Q:

What is the LCM of 124 and 119?

Accepted Solution

A:
Solution: The LCM of 124 and 119 is 14756 Methods How to find the LCM of 124 and 119 using Prime Factorization One way to find the LCM of 124 and 119 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 124? What are the Factors of 119? Here is the prime factorization of 124: 2 2 × 3 1 1 2^2 × 31^1 2 2 × 3 1 1 And this is the prime factorization of 119: 7 1 × 1 7 1 7^1 × 17^1 7 1 × 1 7 1 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: 2, 31, 7, 17 2 2 × 7 1 × 1 7 1 × 3 1 1 = 14756 2^2 × 7^1 × 17^1 × 31^1 = 14756 2 2 × 7 1 × 1 7 1 × 3 1 1 = 14756 Through this we see that the LCM of 124 and 119 is 14756. How to Find the LCM of 124 and 119 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 124 and 119 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, 124 and 119: What are the Multiples of 124? What are the Multiples of 119? Let’s take a look at the first 10 multiples for each of these numbers, 124 and 119: First 10 Multiples of 124: 124, 248, 372, 496, 620, 744, 868, 992, 1116, 1240 First 10 Multiples of 119: 119, 238, 357, 476, 595, 714, 833, 952, 1071, 1190 You 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 124 and 119 are 14756, 29512, 44268. Because 14756 is the smallest, it is the least common multiple. The LCM of 124 and 119 is 14756. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 62 and 5? What is the LCM of 85 and 77? What is the LCM of 43 and 149? What is the LCM of 13 and 111? What is the LCM of 100 and 17?