Q:

What is the LCM of 33 and 138?

Accepted Solution

A:
Solution: The LCM of 33 and 138 is 1518 Methods How to find the LCM of 33 and 138 using Prime Factorization One way to find the LCM of 33 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 33? What are the Factors of 138? Here is the prime factorization of 33: 3 1 × 1 1 1 3^1 × 11^1 3 1 × 1 1 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, 11, 2, 23 2 1 × 3 1 × 1 1 1 × 2 3 1 = 1518 2^1 × 3^1 × 11^1 × 23^1 = 1518 2 1 × 3 1 × 1 1 1 × 2 3 1 = 1518 Through this we see that the LCM of 33 and 138 is 1518. How to Find the LCM of 33 and 138 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 33 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, 33 and 138: What are the Multiples of 33? What are the Multiples of 138? Let’s take a look at the first 10 multiples for each of these numbers, 33 and 138: First 10 Multiples of 33: 33, 66, 99, 132, 165, 198, 231, 264, 297, 330 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 33 and 138 are 1518, 3036, 4554. Because 1518 is the smallest, it is the least common multiple. The LCM of 33 and 138 is 1518. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 90 and 41? What is the LCM of 91 and 139? What is the LCM of 2 and 148? What is the LCM of 110 and 75? What is the LCM of 38 and 45?