Solution: The LCM of 46 and 141 is 6486
Methods
How to find the LCM of 46 and 141 using Prime Factorization
One way to find the LCM of 46 and 141 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 46?
What are the Factors of 141?
Here is the prime factorization of 46:
2
1
×
2
3
1
2^1 × 23^1
2 1 × 2 3 1
And this is the prime factorization of 141:
3
1
×
4
7
1
3^1 × 47^1
3 1 × 4 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: 2, 23, 3, 47
2
1
×
3
1
×
2
3
1
×
4
7
1
=
6486
2^1 × 3^1 × 23^1 × 47^1 = 6486
2 1 × 3 1 × 2 3 1 × 4 7 1 = 6486
Through this we see that the LCM of 46 and 141 is 6486.
How to Find the LCM of 46 and 141 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 46 and 141 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, 46 and 141:
What are the Multiples of 46?
What are the Multiples of 141?
Let’s take a look at the first 10 multiples for each of these numbers, 46 and 141:
First 10 Multiples of 46: 46, 92, 138, 184, 230, 276, 322, 368, 414, 460
First 10 Multiples of 141: 141, 282, 423, 564, 705, 846, 987, 1128, 1269, 1410
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 46 and 141 are 6486, 12972, 19458. Because 6486 is the smallest, it is the least common multiple.
The LCM of 46 and 141 is 6486.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 148 and 74?
What is the LCM of 127 and 65?
What is the LCM of 38 and 70?
What is the LCM of 67 and 136?
What is the LCM of 58 and 75?