Solution: The LCM of 42 and 143 is 6006
Methods
How to find the LCM of 42 and 143 using Prime Factorization
One way to find the LCM of 42 and 143 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 42?
What are the Factors of 143?
Here is the prime factorization of 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 1 × 7 1
And this is the prime factorization of 143:
1
1
1
×
1
3
1
11^1 × 13^1
1 1 1 × 1 3 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, 7, 11, 13
2
1
×
3
1
×
7
1
×
1
1
1
×
1
3
1
=
6006
2^1 × 3^1 × 7^1 × 11^1 × 13^1 = 6006
2 1 × 3 1 × 7 1 × 1 1 1 × 1 3 1 = 6006
Through this we see that the LCM of 42 and 143 is 6006.
How to Find the LCM of 42 and 143 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 42 and 143 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, 42 and 143:
What are the Multiples of 42?
What are the Multiples of 143?
Let’s take a look at the first 10 multiples for each of these numbers, 42 and 143:
First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420
First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430
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 42 and 143 are 6006, 12012, 18018. Because 6006 is the smallest, it is the least common multiple.
The LCM of 42 and 143 is 6006.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 45 and 121?
What is the LCM of 25 and 118?
What is the LCM of 31 and 144?
What is the LCM of 98 and 68?
What is the LCM of 59 and 74?