Q:

What is the LCM of 138 and 136?

Accepted Solution

A:
Solution: The LCM of 138 and 136 is 9384 Methods How to find the LCM of 138 and 136 using Prime Factorization One way to find the LCM of 138 and 136 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 136? 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 136: 2 3 × 1 7 1 2^3 × 17^1 2 3 × 1 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, 17 2 3 × 3 1 × 1 7 1 × 2 3 1 = 9384 2^3 × 3^1 × 17^1 × 23^1 = 9384 2 3 × 3 1 × 1 7 1 × 2 3 1 = 9384 Through this we see that the LCM of 138 and 136 is 9384. How to Find the LCM of 138 and 136 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 138 and 136 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 136: What are the Multiples of 138? What are the Multiples of 136? Let’s take a look at the first 10 multiples for each of these numbers, 138 and 136: First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380 First 10 Multiples of 136: 136, 272, 408, 544, 680, 816, 952, 1088, 1224, 1360 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 136 are 9384, 18768, 28152. Because 9384 is the smallest, it is the least common multiple. The LCM of 138 and 136 is 9384. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 122 and 62? What is the LCM of 46 and 70? What is the LCM of 12 and 34? What is the LCM of 59 and 89? What is the LCM of 81 and 75?