Q:

What is the LCM of 42 and 83?

Accepted Solution

A:
Solution: The LCM of 42 and 83 is 3486 Methods How to find the LCM of 42 and 83 using Prime Factorization One way to find the LCM of 42 and 83 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 83? 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 83: 8 3 1 83^1 8 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, 3, 7, 83 2 1 × 3 1 × 7 1 × 8 3 1 = 3486 2^1 × 3^1 × 7^1 × 83^1 = 3486 2 1 × 3 1 × 7 1 × 8 3 1 = 3486 Through this we see that the LCM of 42 and 83 is 3486. How to Find the LCM of 42 and 83 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 42 and 83 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 83: What are the Multiples of 42? What are the Multiples of 83? Let’s take a look at the first 10 multiples for each of these numbers, 42 and 83: First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420 First 10 Multiples of 83: 83, 166, 249, 332, 415, 498, 581, 664, 747, 830 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 83 are 3486, 6972, 10458. Because 3486 is the smallest, it is the least common multiple. The LCM of 42 and 83 is 3486. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 105 and 54? What is the LCM of 60 and 121? What is the LCM of 94 and 40? What is the LCM of 48 and 97? What is the LCM of 35 and 63?