Q:

What is the LCM of 54 and 70?

Accepted Solution

A:
Solution: The LCM of 54 and 70 is 1890 Methods How to find the LCM of 54 and 70 using Prime Factorization One way to find the LCM of 54 and 70 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 54? What are the Factors of 70? Here is the prime factorization of 54: 2 1 × 3 3 2^1 × 3^3 2 1 × 3 3 And this is the prime factorization of 70: 2 1 × 5 1 × 7 1 2^1 × 5^1 × 7^1 2 1 × 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, 5, 7 2 1 × 3 3 × 5 1 × 7 1 = 1890 2^1 × 3^3 × 5^1 × 7^1 = 1890 2 1 × 3 3 × 5 1 × 7 1 = 1890 Through this we see that the LCM of 54 and 70 is 1890. How to Find the LCM of 54 and 70 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 54 and 70 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, 54 and 70: What are the Multiples of 54? What are the Multiples of 70? Let’s take a look at the first 10 multiples for each of these numbers, 54 and 70: First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540 First 10 Multiples of 70: 70, 140, 210, 280, 350, 420, 490, 560, 630, 700 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 54 and 70 are 1890, 3780, 5670. Because 1890 is the smallest, it is the least common multiple. The LCM of 54 and 70 is 1890. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 65 and 14? What is the LCM of 12 and 130? What is the LCM of 113 and 60? What is the LCM of 68 and 48? What is the LCM of 33 and 6?