Q:

What is the LCM of 36 and 89?

Accepted Solution

A:
Solution: The LCM of 36 and 89 is 3204 Methods How to find the LCM of 36 and 89 using Prime Factorization One way to find the LCM of 36 and 89 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 36? What are the Factors of 89? Here is the prime factorization of 36: 2 2 × 3 2 2^2 × 3^2 2 2 × 3 2 And this is the prime factorization of 89: 8 9 1 89^1 8 9 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, 89 2 2 × 3 2 × 8 9 1 = 3204 2^2 × 3^2 × 89^1 = 3204 2 2 × 3 2 × 8 9 1 = 3204 Through this we see that the LCM of 36 and 89 is 3204. How to Find the LCM of 36 and 89 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 36 and 89 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, 36 and 89: What are the Multiples of 36? What are the Multiples of 89? Let’s take a look at the first 10 multiples for each of these numbers, 36 and 89: First 10 Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360 First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890 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 36 and 89 are 3204, 6408, 9612. Because 3204 is the smallest, it is the least common multiple. The LCM of 36 and 89 is 3204. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 134 and 55? What is the LCM of 107 and 68? What is the LCM of 127 and 135? What is the LCM of 99 and 24? What is the LCM of 130 and 43?