Q:

What is the LCM of 135 and 126?

Accepted Solution

A:
Solution: The LCM of 135 and 126 is 1890 Methods How to find the LCM of 135 and 126 using Prime Factorization One way to find the LCM of 135 and 126 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 135? What are the Factors of 126? Here is the prime factorization of 135: 3 3 × 5 1 3^3 × 5^1 3 3 × 5 1 And this is the prime factorization of 126: 2 1 × 3 2 × 7 1 2^1 × 3^2 × 7^1 2 1 × 3 2 × 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: 3, 5, 2, 7 2 1 × 3 3 × 5 1 × 7 1 = 1890 2^1 × 3^3 × 5^1 × 7^1 = 1890 2 1 × 3 3 × 5 1 × 7 1 = 1890 Through this we see that the LCM of 135 and 126 is 1890. How to Find the LCM of 135 and 126 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 135 and 126 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, 135 and 126: What are the Multiples of 135? What are the Multiples of 126? Let’s take a look at the first 10 multiples for each of these numbers, 135 and 126: First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350 First 10 Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260 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 135 and 126 are 1890, 3780, 5670. Because 1890 is the smallest, it is the least common multiple. The LCM of 135 and 126 is 1890. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 100 and 82? What is the LCM of 125 and 108? What is the LCM of 67 and 30? What is the LCM of 144 and 85? What is the LCM of 20 and 56?