Solution: The LCM of 142 and 18 is 1278
Methods
How to find the LCM of 142 and 18 using Prime Factorization
One way to find the LCM of 142 and 18 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 142?
What are the Factors of 18?
Here is the prime factorization of 142:
2
1
×
7
1
1
2^1 × 71^1
2 1 × 7 1 1
And this is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
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, 71, 3
2
1
×
3
2
×
7
1
1
=
1278
2^1 × 3^2 × 71^1 = 1278
2 1 × 3 2 × 7 1 1 = 1278
Through this we see that the LCM of 142 and 18 is 1278.
How to Find the LCM of 142 and 18 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 142 and 18 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, 142 and 18:
What are the Multiples of 142?
What are the Multiples of 18?
Let’s take a look at the first 10 multiples for each of these numbers, 142 and 18:
First 10 Multiples of 142: 142, 284, 426, 568, 710, 852, 994, 1136, 1278, 1420
First 10 Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180
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 142 and 18 are 1278, 2556, 3834. Because 1278 is the smallest, it is the least common multiple.
The LCM of 142 and 18 is 1278.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 52 and 87?
What is the LCM of 59 and 139?
What is the LCM of 43 and 77?
What is the LCM of 71 and 81?
What is the LCM of 68 and 49?