Q:

What is the LCM of 109 and 21?

Accepted Solution

A:
Solution: The LCM of 109 and 21 is 2289 Methods How to find the LCM of 109 and 21 using Prime Factorization One way to find the LCM of 109 and 21 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 21? Here is the prime factorization of 109: 10 9 1 109^1 10 9 1 And this is the prime factorization of 21: 3 1 × 7 1 3^1 × 7^1 3 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: 109, 3, 7 3 1 × 7 1 × 10 9 1 = 2289 3^1 × 7^1 × 109^1 = 2289 3 1 × 7 1 × 10 9 1 = 2289 Through this we see that the LCM of 109 and 21 is 2289. How to Find the LCM of 109 and 21 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 109 and 21 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 21: What are the Multiples of 109? What are the Multiples of 21? Let’s take a look at the first 10 multiples for each of these numbers, 109 and 21: First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090 First 10 Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210 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 21 are 2289, 4578, 6867. Because 2289 is the smallest, it is the least common multiple. The LCM of 109 and 21 is 2289. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 149 and 130? What is the LCM of 98 and 3? What is the LCM of 10 and 143? What is the LCM of 73 and 57? What is the LCM of 113 and 70?