Q:

What is the LCM of 45 and 44?

Accepted Solution

A:
Solution: The LCM of 45 and 44 is 1980 Methods How to find the LCM of 45 and 44 using Prime Factorization One way to find the LCM of 45 and 44 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 45? What are the Factors of 44? Here is the prime factorization of 45: 3 2 × 5 1 3^2 × 5^1 3 2 × 5 1 And this is the prime factorization of 44: 2 2 × 1 1 1 2^2 × 11^1 2 2 × 1 1 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: 3, 5, 2, 11 2 2 × 3 2 × 5 1 × 1 1 1 = 1980 2^2 × 3^2 × 5^1 × 11^1 = 1980 2 2 × 3 2 × 5 1 × 1 1 1 = 1980 Through this we see that the LCM of 45 and 44 is 1980. How to Find the LCM of 45 and 44 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 45 and 44 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, 45 and 44: What are the Multiples of 45? What are the Multiples of 44? Let’s take a look at the first 10 multiples for each of these numbers, 45 and 44: First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450 First 10 Multiples of 44: 44, 88, 132, 176, 220, 264, 308, 352, 396, 440 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 45 and 44 are 1980, 3960, 5940. Because 1980 is the smallest, it is the least common multiple. The LCM of 45 and 44 is 1980. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 85 and 135? What is the LCM of 94 and 10? What is the LCM of 115 and 145? What is the LCM of 13 and 36? What is the LCM of 38 and 108?