Q:

What is the LCM of 45 and 138?

Accepted Solution

A:
Solution: The LCM of 45 and 138 is 2070 Methods How to find the LCM of 45 and 138 using Prime Factorization One way to find the LCM of 45 and 138 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 138? 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 138: 2 1 × 3 1 × 2 3 1 2^1 × 3^1 × 23^1 2 1 × 3 1 × 2 3 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, 23 2 1 × 3 2 × 5 1 × 2 3 1 = 2070 2^1 × 3^2 × 5^1 × 23^1 = 2070 2 1 × 3 2 × 5 1 × 2 3 1 = 2070 Through this we see that the LCM of 45 and 138 is 2070. How to Find the LCM of 45 and 138 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 45 and 138 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 138: What are the Multiples of 45? What are the Multiples of 138? Let’s take a look at the first 10 multiples for each of these numbers, 45 and 138: First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450 First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380 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 138 are 2070, 4140, 6210. Because 2070 is the smallest, it is the least common multiple. The LCM of 45 and 138 is 2070. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 118 and 12? What is the LCM of 40 and 50? What is the LCM of 76 and 23? What is the LCM of 74 and 135? What is the LCM of 120 and 2?