Solution: The LCM of 145 and 14 is 2030
Methods
How to find the LCM of 145 and 14 using Prime Factorization
One way to find the LCM of 145 and 14 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 145?
What are the Factors of 14?
Here is the prime factorization of 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 9 1
And this is the prime factorization of 14:
2
1
×
7
1
2^1 × 7^1
2 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: 5, 29, 2, 7
2
1
×
5
1
×
7
1
×
2
9
1
=
2030
2^1 × 5^1 × 7^1 × 29^1 = 2030
2 1 × 5 1 × 7 1 × 2 9 1 = 2030
Through this we see that the LCM of 145 and 14 is 2030.
How to Find the LCM of 145 and 14 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 145 and 14 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, 145 and 14:
What are the Multiples of 145?
What are the Multiples of 14?
Let’s take a look at the first 10 multiples for each of these numbers, 145 and 14:
First 10 Multiples of 145: 145, 290, 435, 580, 725, 870, 1015, 1160, 1305, 1450
First 10 Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140
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 145 and 14 are 2030, 4060, 6090. Because 2030 is the smallest, it is the least common multiple.
The LCM of 145 and 14 is 2030.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 73 and 48?
What is the LCM of 98 and 124?
What is the LCM of 125 and 18?
What is the LCM of 42 and 133?
What is the LCM of 66 and 147?