Q:

What is the LCM of 42 and 134?

Accepted Solution

A:
Solution: The LCM of 42 and 134 is 2814 Methods How to find the LCM of 42 and 134 using Prime Factorization One way to find the LCM of 42 and 134 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 42? What are the Factors of 134? Here is the prime factorization of 42: 2 1 × 3 1 × 7 1 2^1 × 3^1 × 7^1 2 1 × 3 1 × 7 1 And this is the prime factorization of 134: 2 1 × 6 7 1 2^1 × 67^1 2 1 × 6 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, 7, 67 2 1 × 3 1 × 7 1 × 6 7 1 = 2814 2^1 × 3^1 × 7^1 × 67^1 = 2814 2 1 × 3 1 × 7 1 × 6 7 1 = 2814 Through this we see that the LCM of 42 and 134 is 2814. How to Find the LCM of 42 and 134 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 42 and 134 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, 42 and 134: What are the Multiples of 42? What are the Multiples of 134? Let’s take a look at the first 10 multiples for each of these numbers, 42 and 134: First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420 First 10 Multiples of 134: 134, 268, 402, 536, 670, 804, 938, 1072, 1206, 1340 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 42 and 134 are 2814, 5628, 8442. Because 2814 is the smallest, it is the least common multiple. The LCM of 42 and 134 is 2814. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 127 and 107? What is the LCM of 88 and 60? What is the LCM of 106 and 134? What is the LCM of 58 and 115? What is the LCM of 80 and 20?