Solution: The LCM of 70 and 50 is 350
Methods
How to find the LCM of 70 and 50 using Prime Factorization
One way to find the LCM of 70 and 50 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 70?
What are the Factors of 50?
Here is the prime factorization of 70:
2
1
×
5
1
×
7
1
2^1 × 5^1 × 7^1
2 1 × 5 1 × 7 1
And this is the prime factorization of 50:
2
1
×
5
2
2^1 × 5^2
2 1 × 5 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, 5, 7
2
1
×
5
2
×
7
1
=
350
2^1 × 5^2 × 7^1 = 350
2 1 × 5 2 × 7 1 = 350
Through this we see that the LCM of 70 and 50 is 350.
How to Find the LCM of 70 and 50 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 70 and 50 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, 70 and 50:
What are the Multiples of 70?
What are the Multiples of 50?
Let’s take a look at the first 10 multiples for each of these numbers, 70 and 50:
First 10 Multiples of 70: 70, 140, 210, 280, 350, 420, 490, 560, 630, 700
First 10 Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500
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 70 and 50 are 350, 700, 1050. Because 350 is the smallest, it is the least common multiple.
The LCM of 70 and 50 is 350.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 35 and 110?
What is the LCM of 112 and 76?
What is the LCM of 116 and 32?
What is the LCM of 129 and 59?
What is the LCM of 16 and 135?