Q:

What is the LCM of 56 and 134?

Accepted Solution

A:
Solution: The LCM of 56 and 134 is 3752 Methods How to find the LCM of 56 and 134 using Prime Factorization One way to find the LCM of 56 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 56? What are the Factors of 134? Here is the prime factorization of 56: 2 3 × 7 1 2^3 × 7^1 2 3 × 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, 7, 67 2 3 × 7 1 × 6 7 1 = 3752 2^3 × 7^1 × 67^1 = 3752 2 3 × 7 1 × 6 7 1 = 3752 Through this we see that the LCM of 56 and 134 is 3752. How to Find the LCM of 56 and 134 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 56 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, 56 and 134: What are the Multiples of 56? What are the Multiples of 134? Let’s take a look at the first 10 multiples for each of these numbers, 56 and 134: First 10 Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560 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 56 and 134 are 3752, 7504, 11256. Because 3752 is the smallest, it is the least common multiple. The LCM of 56 and 134 is 3752. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 13 and 112? What is the LCM of 114 and 91? What is the LCM of 33 and 127? What is the LCM of 130 and 54? What is the LCM of 105 and 103?