Q:

What is the LCM of 101 and 103?

Accepted Solution

A:
Solution: The LCM of 101 and 103 is 10403 Methods How to find the LCM of 101 and 103 using Prime Factorization One way to find the LCM of 101 and 103 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 101? What are the Factors of 103? Here is the prime factorization of 101: 10 1 1 101^1 10 1 1 And this is the prime factorization of 103: 10 3 1 103^1 10 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: 101, 103 10 1 1 × 10 3 1 = 10403 101^1 × 103^1 = 10403 10 1 1 × 10 3 1 = 10403 Through this we see that the LCM of 101 and 103 is 10403. How to Find the LCM of 101 and 103 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 101 and 103 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, 101 and 103: What are the Multiples of 101? What are the Multiples of 103? Let’s take a look at the first 10 multiples for each of these numbers, 101 and 103: First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010 First 10 Multiples of 103: 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030 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 101 and 103 are 10403, 20806, 31209. Because 10403 is the smallest, it is the least common multiple. The LCM of 101 and 103 is 10403. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 86 and 131? What is the LCM of 18 and 106? What is the LCM of 137 and 118? What is the LCM of 65 and 3? What is the LCM of 142 and 27?