Q:

What is the LCM of 75 and 62?

Accepted Solution

A:
Solution: The LCM of 75 and 62 is 4650 Methods How to find the LCM of 75 and 62 using Prime Factorization One way to find the LCM of 75 and 62 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 75? What are the Factors of 62? Here is the prime factorization of 75: 3 1 × 5 2 3^1 × 5^2 3 1 × 5 2 And this is the prime factorization of 62: 2 1 × 3 1 1 2^1 × 31^1 2 1 × 3 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: 3, 5, 2, 31 2 1 × 3 1 × 5 2 × 3 1 1 = 4650 2^1 × 3^1 × 5^2 × 31^1 = 4650 2 1 × 3 1 × 5 2 × 3 1 1 = 4650 Through this we see that the LCM of 75 and 62 is 4650. How to Find the LCM of 75 and 62 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 75 and 62 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, 75 and 62: What are the Multiples of 75? What are the Multiples of 62? Let’s take a look at the first 10 multiples for each of these numbers, 75 and 62: First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750 First 10 Multiples of 62: 62, 124, 186, 248, 310, 372, 434, 496, 558, 620 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 75 and 62 are 4650, 9300, 13950. Because 4650 is the smallest, it is the least common multiple. The LCM of 75 and 62 is 4650. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 94 and 28? What is the LCM of 76 and 149? What is the LCM of 48 and 85? What is the LCM of 1 and 2? What is the LCM of 124 and 8?