Q:

What is the LCM of 65 and 122?

Accepted Solution

A:
Solution: The LCM of 65 and 122 is 7930 Methods How to find the LCM of 65 and 122 using Prime Factorization One way to find the LCM of 65 and 122 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 65? What are the Factors of 122? Here is the prime factorization of 65: 5 1 × 1 3 1 5^1 × 13^1 5 1 × 1 3 1 And this is the prime factorization of 122: 2 1 × 6 1 1 2^1 × 61^1 2 1 × 6 1 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: 5, 13, 2, 61 2 1 × 5 1 × 1 3 1 × 6 1 1 = 7930 2^1 × 5^1 × 13^1 × 61^1 = 7930 2 1 × 5 1 × 1 3 1 × 6 1 1 = 7930 Through this we see that the LCM of 65 and 122 is 7930. How to Find the LCM of 65 and 122 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 65 and 122 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, 65 and 122: What are the Multiples of 65? What are the Multiples of 122? Let’s take a look at the first 10 multiples for each of these numbers, 65 and 122: First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650 First 10 Multiples of 122: 122, 244, 366, 488, 610, 732, 854, 976, 1098, 1220 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 65 and 122 are 7930, 15860, 23790. Because 7930 is the smallest, it is the least common multiple. The LCM of 65 and 122 is 7930. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 42 and 140? What is the LCM of 44 and 64? What is the LCM of 29 and 33? What is the LCM of 142 and 81? What is the LCM of 143 and 116?