Q:

What is the LCM of 109 and 114?

Accepted Solution

A:
Solution: The LCM of 109 and 114 is 12426 Methods How to find the LCM of 109 and 114 using Prime Factorization One way to find the LCM of 109 and 114 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 109? What are the Factors of 114? Here is the prime factorization of 109: 10 9 1 109^1 10 9 1 And this 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 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: 109, 2, 3, 19 2 1 × 3 1 × 1 9 1 × 10 9 1 = 12426 2^1 × 3^1 × 19^1 × 109^1 = 12426 2 1 × 3 1 × 1 9 1 × 10 9 1 = 12426 Through this we see that the LCM of 109 and 114 is 12426. How to Find the LCM of 109 and 114 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 109 and 114 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, 109 and 114: What are the Multiples of 109? What are the Multiples of 114? Let’s take a look at the first 10 multiples for each of these numbers, 109 and 114: First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090 First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140 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 109 and 114 are 12426, 24852, 37278. Because 12426 is the smallest, it is the least common multiple. The LCM of 109 and 114 is 12426. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 69 and 29? What is the LCM of 23 and 110? What is the LCM of 127 and 48? What is the LCM of 11 and 16? What is the LCM of 5 and 144?