Q:

What is the LCM of 34 and 36?

Accepted Solution

A:
Solution: The LCM of 34 and 36 is 612 Methods How to find the LCM of 34 and 36 using Prime Factorization One way to find the LCM of 34 and 36 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 34? What are the Factors of 36? Here is the prime factorization of 34: 2 1 × 1 7 1 2^1 × 17^1 2 1 × 1 7 1 And this is the prime factorization of 36: 2 2 × 3 2 2^2 × 3^2 2 2 × 3 2 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, 17, 3 2 2 × 3 2 × 1 7 1 = 612 2^2 × 3^2 × 17^1 = 612 2 2 × 3 2 × 1 7 1 = 612 Through this we see that the LCM of 34 and 36 is 612. How to Find the LCM of 34 and 36 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 34 and 36 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, 34 and 36: What are the Multiples of 34? What are the Multiples of 36? Let’s take a look at the first 10 multiples for each of these numbers, 34 and 36: First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340 First 10 Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360 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 34 and 36 are 612, 1224, 1836. Because 612 is the smallest, it is the least common multiple. The LCM of 34 and 36 is 612. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 57 and 102? What is the LCM of 97 and 13? What is the LCM of 120 and 66? What is the LCM of 100 and 83? What is the LCM of 21 and 55?