Q:

What is the LCM of 42 and 105?

Accepted Solution

A:
Solution: The LCM of 42 and 105 is 210 Methods How to find the LCM of 42 and 105 using Prime Factorization One way to find the LCM of 42 and 105 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 105? Here is the prime factorization of 42: 2 1 Γ— 3 1 Γ— 7 1 2^1 Γ— 3^1 Γ— 7^1 2 1 Γ— 3 1 Γ— 7 1 And this is the prime factorization of 105: 3 1 Γ— 5 1 Γ— 7 1 3^1 Γ— 5^1 Γ— 7^1 3 1 Γ— 5 1 Γ— 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, 5 2 1 Γ— 3 1 Γ— 5 1 Γ— 7 1 = 210 2^1 Γ— 3^1 Γ— 5^1 Γ— 7^1 = 210 2 1 Γ— 3 1 Γ— 5 1 Γ— 7 1 = 210 Through this we see that the LCM of 42 and 105 is 210. How to Find the LCM of 42 and 105 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 42 and 105 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 105: What are the Multiples of 42? What are the Multiples of 105? Let’s take a look at the first 10 multiples for each of these numbers, 42 and 105: First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420 First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050 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 105 are 210, 420, 630. Because 210 is the smallest, it is the least common multiple. The LCM of 42 and 105 is 210. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 80 and 66? What is the LCM of 136 and 150? What is the LCM of 106 and 76? What is the LCM of 19 and 115? What is the LCM of 140 and 24?