Q:

What is the LCM of 78 and 140?

Accepted Solution

A:
Solution: The LCM of 78 and 140 is 5460 Methods How to find the LCM of 78 and 140 using Prime Factorization One way to find the LCM of 78 and 140 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 78? What are the Factors of 140? Here 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 And this is the prime factorization of 140: 2 2 × 5 1 × 7 1 2^2 × 5^1 × 7^1 2 2 × 5 1 × 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, 13, 5, 7 2 2 × 3 1 × 5 1 × 7 1 × 1 3 1 = 5460 2^2 × 3^1 × 5^1 × 7^1 × 13^1 = 5460 2 2 × 3 1 × 5 1 × 7 1 × 1 3 1 = 5460 Through this we see that the LCM of 78 and 140 is 5460. How to Find the LCM of 78 and 140 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 78 and 140 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, 78 and 140: What are the Multiples of 78? What are the Multiples of 140? Let’s take a look at the first 10 multiples for each of these numbers, 78 and 140: First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780 First 10 Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400 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 78 and 140 are 5460, 10920, 16380. Because 5460 is the smallest, it is the least common multiple. The LCM of 78 and 140 is 5460. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 110 and 61? What is the LCM of 139 and 123? What is the LCM of 95 and 60? What is the LCM of 116 and 39? What is the LCM of 31 and 21?