Q:

What is the LCM of 109 and 45?

Accepted Solution

A:
Solution: The LCM of 109 and 45 is 4905 Methods How to find the LCM of 109 and 45 using Prime Factorization One way to find the LCM of 109 and 45 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 45? Here is the prime factorization of 109: 10 9 1 109^1 10 9 1 And this is the prime factorization of 45: 3 2 × 5 1 3^2 × 5^1 3 2 × 5 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, 5 3 2 × 5 1 × 10 9 1 = 4905 3^2 × 5^1 × 109^1 = 4905 3 2 × 5 1 × 10 9 1 = 4905 Through this we see that the LCM of 109 and 45 is 4905. How to Find the LCM of 109 and 45 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 109 and 45 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 45: What are the Multiples of 109? What are the Multiples of 45? Let’s take a look at the first 10 multiples for each of these numbers, 109 and 45: First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090 First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450 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 45 are 4905, 9810, 14715. Because 4905 is the smallest, it is the least common multiple. The LCM of 109 and 45 is 4905. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 12 and 59? What is the LCM of 127 and 138? What is the LCM of 11 and 50? What is the LCM of 61 and 21? What is the LCM of 91 and 72?