Q:

What is the LCM of 120 and 42?

Accepted Solution

A:
Solution: The LCM of 120 and 42 is 840 Methods How to find the LCM of 120 and 42 using Prime Factorization One way to find the LCM of 120 and 42 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 120? What are the Factors of 42? Here is the prime factorization of 120: 2 3 Γ— 3 1 Γ— 5 1 2^3 Γ— 3^1 Γ— 5^1 2 3 Γ— 3 1 Γ— 5 1 And this 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 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, 5, 7 2 3 Γ— 3 1 Γ— 5 1 Γ— 7 1 = 840 2^3 Γ— 3^1 Γ— 5^1 Γ— 7^1 = 840 2 3 Γ— 3 1 Γ— 5 1 Γ— 7 1 = 840 Through this we see that the LCM of 120 and 42 is 840. How to Find the LCM of 120 and 42 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 120 and 42 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, 120 and 42: What are the Multiples of 120? What are the Multiples of 42? Let’s take a look at the first 10 multiples for each of these numbers, 120 and 42: First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200 First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420 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 120 and 42 are 840, 1680, 2520. Because 840 is the smallest, it is the least common multiple. The LCM of 120 and 42 is 840. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 65 and 19? What is the LCM of 143 and 67? What is the LCM of 115 and 34? What is the LCM of 40 and 53? What is the LCM of 147 and 87?