How to find the Least Common Multiple Worksheet, Examples, and Definition

What is the Least Common Multiple?

The Least Common Multiple (LCM) is a mathematical concept used to find the smallest common multiple of two or more numbers. In math, numbers are often used to represent real-world quantities, and finding the LCM helps to simplify mathematical operations involving those numbers.

To find the LCM of two or more numbers, one can list the multiples of each number and then identify the smallest multiple that is common to all of them. This process is often used in elementary math classes and is an important skill for solving more complex problems in algebra and other branches of mathematics.

Understanding the concept of LCM is important for students of all ages, as it lays the foundation for more advanced mathematical concepts. By mastering the techniques for finding the LCM of two or more numbers, students can develop a deeper understanding of mathematical operations and improve their problem-solving skills.

The Least Common Multiple is the smallest number is that a multiple of both original numbers. A common multiple is any number that is a multiple of both original numbers. One way to find the Least Common Multiple is to list out the multiples of each number until you find a number that is a multiple of both numbers. Another way to find the Least Common Multiple is to factor each number into prime factors. Then you multiply the largest set of each factor together with all the other largest sets of each factor.

Common Core Standard: 6.NS.4
Related Topics: Adding Decimals, Subtracting Decimals, Multiplying Decimals, Dividing Decimals, Greatest Common Factor
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Least Common Multiple Definition

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more numbers. In other words, it is the lowest common multiple of a set of numbers. The LCM is also known as the lowest common denominator or smallest common multiple.

To find the LCM of two or more numbers, you need to identify their common multiples, which are the multiples that they share. The LCM is then the smallest of these common multiples. For example, the LCM of 3 and 4 is 12, because 12 is the smallest number that is a multiple of both 3 and 4.

The LCM is an important concept in mathematics, particularly in number theory and algebra. It is used in various applications, such as simplifying fractions, adding and subtracting fractions with different denominators, and solving equations involving fractions.

Calculating the LCM can be done using different methods, such as the prime factorization method, the listing method, or the division method. The prime factorization method involves finding the prime factors of each number and multiplying them together, while the listing method involves listing the multiples of each number until a common multiple is found. The division method involves dividing each number by their greatest common divisor (GCD) and multiplying the quotients together.

In conclusion, the least common multiple is the smallest positive integer that is a multiple of two or more numbers. It is an essential concept in mathematics and has various applications in different fields.

5 Quick Least Common Multiple Practice Problems

LCM FAQ

What is the difference between LCM and GCD?

The LCM (Least Common Multiple) is the smallest number that is a multiple of two or more numbers, while the GCD (Greatest Common Divisor) is the largest number that divides two or more numbers without leaving a remainder.

How do you find the LCM of two numbers?

To find the LCM of two numbers, you can list the multiples of each number until you find the smallest multiple that they have in common. Alternatively, you can use the prime factorization method, where you find the prime factors of each number and then multiply the highest power of each prime factor together.

What is the LCM of prime numbers?

The LCM of two prime numbers is the product of those two numbers. For example, the LCM of 3 and 5 is 15.

Can LCM of three numbers be zero?

No, the LCM of three numbers cannot be zero. The LCM is always a positive number, and it is only zero if one or more of the numbers is zero.

What is the LCM of fractions?

To find the LCM of fractions, you need to find the LCM of the denominators and then use that as the denominator for the resulting fraction. For example, the LCM of 2/3 and 3/4 is 12, so you can convert the fractions to 8/12 and 9/12, respectively.

What is the LCM of decimals?

Decimals are not typically used in LCM calculations, as LCM is usually used for whole numbers. However, if you need to find the LCM of decimals, you can convert them to fractions and then find the LCM of the resulting fractions.

How to do Least Common Multiple?

To find the LCM of two or more numbers, you can use either the listing method or the prime factorization method. The listing method involves listing the multiples of each number until you find the smallest multiple that they have in common. The prime factorization method involves finding the prime factors of each number and then multiplying the highest power of each prime factor together.

Least Common Multiple Worksheet Video Explanation

Watch our free video on finding Least Common Multiple. This video shows how to solve problems that are on our free Least Common Multiples worksheet that you can get by submitting your email above.

Watch the free Least Common Multiple video on YouTube here: Least Common Multiple Video

Video Transcript:

This video is about how to find least common multiple​. You can get the lowest common multiple worksheet used in this video for free by clicking on the link in the description below. The least common multiple definition states that the least common multiple is the smallest multiple that both numbers have in common. We’re going to do a quick example finding the least common multiple meaning between the numbers 4 and 6. Now I can take both 4 and 6 and I can list out the multiples of each number. We’re going to start with 4. 4 is a multiple 8 is a multiple 12. 4 times 4 16 20 and then 24. We’ll go to and then I can do the same thing for 6. We start with 6 and then we go to 12, then we go to 18 but I don’t have to go any further because I can look and I can see that the number 12 is a multiple of four and six and it is the smallest multiple that they have in common. I know that the least common multiple between four and six would be 12.

You can do the same thing for larger numbers by using factor trees and that’s what I’m going to do for finding the least common multiple between 50 and 20. I’m going to first take 50 and I’m going to break it down by prime factorization. Prime factorization is sometimes shown as a factor tree which is what I’m going to do here. What we’re going to do is we’re going to take each number and break it down into prime factors. The number 50 I know is even so I’m going to divide by 2 2 times 25 gives us 50. Now I know 2 is a prime number. I don’t have to break it down any further but 25 can be broken down into five times five. The fives are also prime numbers which means they cannot be broken down any further. 50 is done because all that we have are prime numbers we’re going to do the same thing for number 20. 20 is an even number I’m going to start with 2. 2 times 10 is 20. 10 is also an even number. i’m going to use 2 again and 2 times 5 is 10. 2 and 5 are also prime numbers so I know that 20 has been broken down completely into prime numbers. I’m going to highlight all of my factors for 50 and all of my factors for 20. Now what I’m going to do is I’m going to take both numbers and I’m going to list them out in their prime factorization. 50 is 2 times 5 times 5 and 20 is 2 times 2 times five. Now when you are looking for your least common multiple, you’re going to use each factor and you’re going to use the largest amount of each factor. When you’re finding the least common multiple you have to use each prime number and you have to use the largest amount of each prime number. For example, if you look, we have both the number 2 and the number 5 is our prime numbers that we have from our factoring. We have to use two when we multiply them all together to get the least common multiple and we also have to use five now we’re going to use two twos because 20 has two twos in it, which is the largest amount of twos, and then we’re going to use five times five because 50 has two fives in it now 50 also has a single 2 and 20 has a single five but we don’t use these because we’ve already used our prime factor of two and our prime factor of five and we took two twos from 20 and two fives from 50. Now to get our answer we just multiply two times two which is four. Four times five is twenty, twenty times five is one hundred. Our least common multiple between fifty and twenty is going to be one hundred.

Let’s do a couple practice problems from our common multiples worksheet. Number one gives us the numbers 12 and 40 and asked us to find the least common multiple between the two. I’m going to start by factoring the number 12 and the number 40. When I factor 12, 12 is an even number. I’m going to start with 2, 2 times 6 is 12, then 6 is also an even number. I’m going to use 2 again and then 2 times 3 is 6. Now 12 has been factored into prime numbers. 2 2 and 3 are all prime I’m going to do the same thing for 40. I’m going to start with a 2 because 40 is even 2 times 20. 20 is even again so I’m going to use 2. 2 times 10, 10 is even so I’m going to use 2 and then 2 times 5 is 10. Now we have 40 broken down into prime factors. These are all prime numbers and 12 is also broken down into prime numbers I’m going to list both of them out 12 is 2 times 2 times 3 and 40 is 2 times 2 times two times five. To get the least common multiple I’m going to use each prime factor once and I’m going to use the largest amount of each prime factor. If you look 12 has two twos but 40 has three twos. I’m going to use these three twos for a least common multiple. I’m going to include 2 times 2 times 2 but I also have to use this 3 because I have to use each factor. I’m going to use a 3 and I have to use this 5. I’m also going to include the 5. To get the least common multiple I’m going to multiply 2 times 2 times 2 times three times five and when I do that, I get 120 as the solution to our least common multiple between 12 and 40.

The next problem on our least common multiple worksheets is number three and that gives us 25 and 80. For this least common multiple example we’re going to do the same thing which is we’re going to take each number and we’re going to break each number down into prime factors. I’m going to take 25 and break it down into 5 times 5. Those are our two prime factors and I know that I’m done because these are both prime numbers. 25 is kind of easy 80 we’re going to break down we’re going to start with 2. 2 times 40 then we’re going to do 2 times 20 to get 40 and then we have to do 20 again. This is 2 times 10 and then 10 is broken down into 2 times five. I’m going to take each number and I’m going to list the prime factors from each number out. We have 25 and we’re going to say 25 is 5 times 5 and I’m going to take 80 and for 80 I’m going to say 80 is 2 times 2 times 2 times 2 times 5. To get the least common multiple that means I have to take each prime factor and the largest amount of each prime factor and multiply them together. In this example we only have two and five so I’m going to use all the twos from 80. This is going to be 2 times 2 times two times two and I’m going to use two fives from 25. This is going to be times five times five now I do not use this five because we already used the two fives from 25. That just sits there we don’t have to use it then to get our least common multiple. I’m going to multiply 2 times 2 times 2 times 2 times 5 times 5 and we will get 400 as the least common multiple between 25 and 80. Hopefully this video is helpful for teaching you how to find the least common multiple. Try all the practice problems by downloading the free finding lcm worksheet above.