Solution: The LCM of 143 and 105 is 15015
Methods
How to find the LCM of 143 and 105 using Prime Factorization
One way to find the LCM of 143 and 105 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 105?
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 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 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: 11, 13, 3, 5, 7
3
1
×
5
1
×
7
1
×
1
1
1
×
1
3
1
=
15015
3^1 × 5^1 × 7^1 × 11^1 × 13^1 = 15015
3 1 × 5 1 × 7 1 × 1 1 1 × 1 3 1 = 15015
Through this we see that the LCM of 143 and 105 is 15015.
How to Find the LCM of 143 and 105 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 143 and 105 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 105:
What are the Multiples of 143?
What are the Multiples of 105?
Let’s take a look at the first 10 multiples for each of these numbers, 143 and 105:
First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
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 105 are 15015, 30030, 45045. Because 15015 is the smallest, it is the least common multiple.
The LCM of 143 and 105 is 15015.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 140 and 122?
What is the LCM of 22 and 64?
What is the LCM of 18 and 75?
What is the LCM of 46 and 126?
What is the LCM of 28 and 62?