Solution: The LCM of 143 and 102 is 14586
Methods
How to find the LCM of 143 and 102 using Prime Factorization
One way to find the LCM of 143 and 102 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 102?
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 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 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, 2, 3, 17
2
1
×
3
1
×
1
1
1
×
1
3
1
×
1
7
1
=
14586
2^1 × 3^1 × 11^1 × 13^1 × 17^1 = 14586
2 1 × 3 1 × 1 1 1 × 1 3 1 × 1 7 1 = 14586
Through this we see that the LCM of 143 and 102 is 14586.
How to Find the LCM of 143 and 102 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 143 and 102 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 102:
What are the Multiples of 143?
What are the Multiples of 102?
Let’s take a look at the first 10 multiples for each of these numbers, 143 and 102:
First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430
First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020
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 102 are 14586, 29172, 43758. Because 14586 is the smallest, it is the least common multiple.
The LCM of 143 and 102 is 14586.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 77 and 68?
What is the LCM of 51 and 122?
What is the LCM of 129 and 14?
What is the LCM of 19 and 148?
What is the LCM of 130 and 89?