Q:

What is the LCM of 120 and 67?

Accepted Solution

A:
Solution: The LCM of 120 and 67 is 8040 Methods How to find the LCM of 120 and 67 using Prime Factorization One way to find the LCM of 120 and 67 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 67? Here is the prime factorization of 120: 2 3 × 3 1 × 5 1 2^3 × 3^1 × 5^1 2 3 × 3 1 × 5 1 And this is the prime factorization of 67: 6 7 1 67^1 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, 3, 5, 67 2 3 × 3 1 × 5 1 × 6 7 1 = 8040 2^3 × 3^1 × 5^1 × 67^1 = 8040 2 3 × 3 1 × 5 1 × 6 7 1 = 8040 Through this we see that the LCM of 120 and 67 is 8040. How to Find the LCM of 120 and 67 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 120 and 67 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 67: What are the Multiples of 120? What are the Multiples of 67? Let’s take a look at the first 10 multiples for each of these numbers, 120 and 67: First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200 First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670 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 67 are 8040, 16080, 24120. Because 8040 is the smallest, it is the least common multiple. The LCM of 120 and 67 is 8040. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 70 and 76? What is the LCM of 41 and 127? What is the LCM of 83 and 2? What is the LCM of 95 and 34? What is the LCM of 61 and 7?