Q:

What is the LCM of 114 and 139?

Accepted Solution

A:
Solution: The LCM of 114 and 139 is 15846 Methods How to find the LCM of 114 and 139 using Prime Factorization One way to find the LCM of 114 and 139 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 114? What are the Factors of 139? Here is the prime factorization of 114: 2 1 × 3 1 × 1 9 1 2^1 × 3^1 × 19^1 2 1 × 3 1 × 1 9 1 And this is the prime factorization of 139: 13 9 1 139^1 13 9 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, 3, 19, 139 2 1 × 3 1 × 1 9 1 × 13 9 1 = 15846 2^1 × 3^1 × 19^1 × 139^1 = 15846 2 1 × 3 1 × 1 9 1 × 13 9 1 = 15846 Through this we see that the LCM of 114 and 139 is 15846. How to Find the LCM of 114 and 139 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 114 and 139 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, 114 and 139: What are the Multiples of 114? What are the Multiples of 139? Let’s take a look at the first 10 multiples for each of these numbers, 114 and 139: First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140 First 10 Multiples of 139: 139, 278, 417, 556, 695, 834, 973, 1112, 1251, 1390 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 114 and 139 are 15846, 31692, 47538. Because 15846 is the smallest, it is the least common multiple. The LCM of 114 and 139 is 15846. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 136 and 74? What is the LCM of 123 and 94? What is the LCM of 33 and 102? What is the LCM of 120 and 26? What is the LCM of 86 and 36?