Q:

What is the LCM of 121 and 78?

Accepted Solution

A:
Solution: The LCM of 121 and 78 is 9438 Methods How to find the LCM of 121 and 78 using Prime Factorization One way to find the LCM of 121 and 78 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 121? What are the Factors of 78? Here is the prime factorization of 121: 1 1 2 11^2 1 1 2 And this is the prime factorization of 78: 2 1 × 3 1 × 1 3 1 2^1 × 3^1 × 13^1 2 1 × 3 1 × 1 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: 11, 2, 3, 13 2 1 × 3 1 × 1 1 2 × 1 3 1 = 9438 2^1 × 3^1 × 11^2 × 13^1 = 9438 2 1 × 3 1 × 1 1 2 × 1 3 1 = 9438 Through this we see that the LCM of 121 and 78 is 9438. How to Find the LCM of 121 and 78 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 121 and 78 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, 121 and 78: What are the Multiples of 121? What are the Multiples of 78? Let’s take a look at the first 10 multiples for each of these numbers, 121 and 78: First 10 Multiples of 121: 121, 242, 363, 484, 605, 726, 847, 968, 1089, 1210 First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780 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 121 and 78 are 9438, 18876, 28314. Because 9438 is the smallest, it is the least common multiple. The LCM of 121 and 78 is 9438. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 37 and 78? What is the LCM of 96 and 133? What is the LCM of 123 and 49? What is the LCM of 39 and 132? What is the LCM of 48 and 139?