Q:

What is the LCM of 57 and 140?

Accepted Solution

A:
Solution: The LCM of 57 and 140 is 7980MethodsHow to find the LCM of 57 and 140 using Prime FactorizationOne way to find the LCM of 57 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 57?What are the Factors of 140?Here is the prime factorization of 57:31×1913^1 × 19^131×191And this is the prime factorization of 140:22×51×712^2 × 5^1 × 7^122×51×71When 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: 3, 19, 2, 5, 722×31×51×71×191=79802^2 × 3^1 × 5^1 × 7^1 × 19^1 = 798022×31×51×71×191=7980Through this we see that the LCM of 57 and 140 is 7980.How to Find the LCM of 57 and 140 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 57 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, 57 and 140:What are the Multiples of 57?What are the Multiples of 140?Let’s take a look at the first 10 multiples for each of these numbers, 57 and 140:First 10 Multiples of 57: 57, 114, 171, 228, 285, 342, 399, 456, 513, 570First 10 Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400You 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 57 and 140 are 7980, 15960, 23940. Because 7980 is the smallest, it is the least common multiple.The LCM of 57 and 140 is 7980.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 142 and 134?What is the LCM of 21 and 68?What is the LCM of 24 and 5?What is the LCM of 23 and 75?What is the LCM of 137 and 95?