Solution: The LCM of 149 and 42 is 6258
Methods
How to find the LCM of 149 and 42 using Prime Factorization
One way to find the LCM of 149 and 42 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 149?
What are the Factors of 42?
Here is the prime factorization of 149:
14
9
1
149^1
14 9 1
And this is the prime factorization of 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 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: 149, 2, 3, 7
2
1
×
3
1
×
7
1
×
14
9
1
=
6258
2^1 × 3^1 × 7^1 × 149^1 = 6258
2 1 × 3 1 × 7 1 × 14 9 1 = 6258
Through this we see that the LCM of 149 and 42 is 6258.
How to Find the LCM of 149 and 42 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 149 and 42 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, 149 and 42:
What are the Multiples of 149?
What are the Multiples of 42?
Let’s take a look at the first 10 multiples for each of these numbers, 149 and 42:
First 10 Multiples of 149: 149, 298, 447, 596, 745, 894, 1043, 1192, 1341, 1490
First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420
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 149 and 42 are 6258, 12516, 18774. Because 6258 is the smallest, it is the least common multiple.
The LCM of 149 and 42 is 6258.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 82 and 6?
What is the LCM of 96 and 60?
What is the LCM of 134 and 63?
What is the LCM of 124 and 79?
What is the LCM of 68 and 45?