Q:

What is the LCM of 138 and 132?

Accepted Solution

A:
Solution: The LCM of 138 and 132 is 3036 Methods How to find the LCM of 138 and 132 using Prime Factorization One way to find the LCM of 138 and 132 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 132? 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 132: 2 2 × 3 1 × 1 1 1 2^2 × 3^1 × 11^1 2 2 × 3 1 × 1 1 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, 11 2 2 × 3 1 × 1 1 1 × 2 3 1 = 3036 2^2 × 3^1 × 11^1 × 23^1 = 3036 2 2 × 3 1 × 1 1 1 × 2 3 1 = 3036 Through this we see that the LCM of 138 and 132 is 3036. How to Find the LCM of 138 and 132 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 138 and 132 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 132: What are the Multiples of 138? What are the Multiples of 132? Let’s take a look at the first 10 multiples for each of these numbers, 138 and 132: First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380 First 10 Multiples of 132: 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320 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 132 are 3036, 6072, 9108. Because 3036 is the smallest, it is the least common multiple. The LCM of 138 and 132 is 3036. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 41 and 150? What is the LCM of 74 and 96? What is the LCM of 54 and 35? What is the LCM of 33 and 149? What is the LCM of 140 and 68?