Q:

What is the LCM of 73 and 145?

Accepted Solution

A:
Solution: The LCM of 73 and 145 is 10585 Methods How to find the LCM of 73 and 145 using Prime Factorization One way to find the LCM of 73 and 145 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 73? What are the Factors of 145? Here is the prime factorization of 73: 7 3 1 73^1 7 3 1 And this is the prime factorization of 145: 5 1 × 2 9 1 5^1 × 29^1 5 1 × 2 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: 73, 5, 29 5 1 × 2 9 1 × 7 3 1 = 10585 5^1 × 29^1 × 73^1 = 10585 5 1 × 2 9 1 × 7 3 1 = 10585 Through this we see that the LCM of 73 and 145 is 10585. How to Find the LCM of 73 and 145 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 73 and 145 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, 73 and 145: What are the Multiples of 73? What are the Multiples of 145? Let’s take a look at the first 10 multiples for each of these numbers, 73 and 145: First 10 Multiples of 73: 73, 146, 219, 292, 365, 438, 511, 584, 657, 730 First 10 Multiples of 145: 145, 290, 435, 580, 725, 870, 1015, 1160, 1305, 1450 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 73 and 145 are 10585, 21170, 31755. Because 10585 is the smallest, it is the least common multiple. The LCM of 73 and 145 is 10585. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 25 and 120? What is the LCM of 127 and 140? What is the LCM of 44 and 14? What is the LCM of 56 and 38? What is the LCM of 115 and 116?