Solution: The LCM of 143 and 145 is 20735
Methods
How to find the LCM of 143 and 145 using Prime Factorization
One way to find the LCM of 143 and 145 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 143?
What are the Factors of 145?
Here is the prime factorization of 143:
1
1
1
×
1
3
1
11^1 × 13^1
1 1 1 × 1 3 1
And this is the prime factorization of 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 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: 11, 13, 5, 29
5
1
×
1
1
1
×
1
3
1
×
2
9
1
=
20735
5^1 × 11^1 × 13^1 × 29^1 = 20735
5 1 × 1 1 1 × 1 3 1 × 2 9 1 = 20735
Through this we see that the LCM of 143 and 145 is 20735.
How to Find the LCM of 143 and 145 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 143 and 145 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, 143 and 145:
What are the Multiples of 143?
What are the Multiples of 145?
Let’s take a look at the first 10 multiples for each of these numbers, 143 and 145:
First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430
First 10 Multiples of 145: 145, 290, 435, 580, 725, 870, 1015, 1160, 1305, 1450
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 143 and 145 are 20735, 41470, 62205. Because 20735 is the smallest, it is the least common multiple.
The LCM of 143 and 145 is 20735.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 49 and 77?
What is the LCM of 29 and 62?
What is the LCM of 95 and 15?
What is the LCM of 83 and 86?
What is the LCM of 97 and 129?