Q:

What is the LCM of 138 and 97?

Accepted Solution

A:
Solution: The LCM of 138 and 97 is 13386 Methods How to find the LCM of 138 and 97 using Prime Factorization One way to find the LCM of 138 and 97 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 138? What are the Factors of 97? Here 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 And this is the prime factorization of 97: 9 7 1 97^1 9 7 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: 2, 3, 23, 97 2 1 × 3 1 × 2 3 1 × 9 7 1 = 13386 2^1 × 3^1 × 23^1 × 97^1 = 13386 2 1 × 3 1 × 2 3 1 × 9 7 1 = 13386 Through this we see that the LCM of 138 and 97 is 13386. How to Find the LCM of 138 and 97 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 138 and 97 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, 138 and 97: What are the Multiples of 138? What are the Multiples of 97? Let’s take a look at the first 10 multiples for each of these numbers, 138 and 97: First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380 First 10 Multiples of 97: 97, 194, 291, 388, 485, 582, 679, 776, 873, 970 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 138 and 97 are 13386, 26772, 40158. Because 13386 is the smallest, it is the least common multiple. The LCM of 138 and 97 is 13386. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 93 and 119? What is the LCM of 120 and 81? What is the LCM of 140 and 43? What is the LCM of 103 and 59? What is the LCM of 44 and 18?