Q:

What is the LCM of 146 and 43?

Accepted Solution

A:
Solution: The LCM of 146 and 43 is 6278 Methods How to find the LCM of 146 and 43 using Prime Factorization One way to find the LCM of 146 and 43 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 146? What are the Factors of 43? Here is the prime factorization of 146: 2 1 Γ— 7 3 1 2^1 Γ— 73^1 2 1 Γ— 7 3 1 And this is the prime factorization of 43: 4 3 1 43^1 4 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: 2, 73, 43 2 1 Γ— 4 3 1 Γ— 7 3 1 = 6278 2^1 Γ— 43^1 Γ— 73^1 = 6278 2 1 Γ— 4 3 1 Γ— 7 3 1 = 6278 Through this we see that the LCM of 146 and 43 is 6278. How to Find the LCM of 146 and 43 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 146 and 43 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, 146 and 43: What are the Multiples of 146? What are the Multiples of 43? Let’s take a look at the first 10 multiples for each of these numbers, 146 and 43: First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460 First 10 Multiples of 43: 43, 86, 129, 172, 215, 258, 301, 344, 387, 430 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 146 and 43 are 6278, 12556, 18834. Because 6278 is the smallest, it is the least common multiple. The LCM of 146 and 43 is 6278. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 30 and 132? What is the LCM of 10 and 77? What is the LCM of 121 and 4? What is the LCM of 103 and 26? What is the LCM of 133 and 48?