Q:

What is the LCM of 140 and 77?

Accepted Solution

A:
Solution: The LCM of 140 and 77 is 1540 Methods How to find the LCM of 140 and 77 using Prime Factorization One way to find the LCM of 140 and 77 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 140? What are the Factors of 77? Here is the prime factorization of 140: 2 2 × 5 1 × 7 1 2^2 × 5^1 × 7^1 2 2 × 5 1 × 7 1 And this is the prime factorization of 77: 7 1 × 1 1 1 7^1 × 11^1 7 1 × 1 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: 2, 5, 7, 11 2 2 × 5 1 × 7 1 × 1 1 1 = 1540 2^2 × 5^1 × 7^1 × 11^1 = 1540 2 2 × 5 1 × 7 1 × 1 1 1 = 1540 Through this we see that the LCM of 140 and 77 is 1540. How to Find the LCM of 140 and 77 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 140 and 77 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, 140 and 77: What are the Multiples of 140? What are the Multiples of 77? Let’s take a look at the first 10 multiples for each of these numbers, 140 and 77: First 10 Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400 First 10 Multiples of 77: 77, 154, 231, 308, 385, 462, 539, 616, 693, 770 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 140 and 77 are 1540, 3080, 4620. Because 1540 is the smallest, it is the least common multiple. The LCM of 140 and 77 is 1540. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 7 and 114? What is the LCM of 147 and 130? What is the LCM of 102 and 148? What is the LCM of 128 and 50? What is the LCM of 150 and 90?