October 2, 2025

What Is The Least Common Multiple Lcm

Q: What is the difference between the LCM and the GCD?

The LCM (Least Common Multiple) is the smallest number that two numbers divide into, while the GCD (Greatest Common Divisor) is the largest number that divides both of them. The LCM is always greater than or equal to the numbers, whereas the GCD is always less than or equal to them.

Q: Can the LCM of two numbers be one of the numbers itself?

Yes. If one number is a multiple of the other, the LCM will be the larger of the two numbers. For example, the LCM of 5 and 10 is 10.

Q: How do you find the LCM of three or more numbers?

The methods are the same. You can list the multiples for all numbers and find the first common one, or you can use the prime factorization method. For the prime factorization method, you multiply the highest power of every prime factor present in any of the numbers.

Q: Is there a formula connecting LCM and GCD?

Yes, for two positive integers 'a' and 'b', the formula is: LCM(a, b) × GCD(a, b) = a × b. This provides a quick way to find the LCM if you already know the GCD.

Learn what the Least Common Multiple (LCM) is, how to find it, and why it's a fundamental concept in mathematics for working with fractions.

Have More Questions →

What Is the Least Common Multiple?

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of all of them. In simpler terms, it's the smallest number that all the given numbers can divide into evenly.

Section 2: How to Find the LCM

There are two common methods to find the LCM. The first is to list the multiples of each number until you find the first one they have in common. The second, more efficient method for larger numbers is to use prime factorization. You find the prime factors of each number, then multiply the highest power of each prime factor that appears in any of the factorizations.

Section 3: A Practical Example

Let's find the LCM of 6 and 8. Using the listing method, the multiples of 6 are 6, 12, 18, 24, 30... The multiples of 8 are 8, 16, 24, 32... The first number to appear in both lists is 24. Therefore, the LCM of 6 and 8 is 24.

Section 4: Why is the LCM Important?

The most common application of the LCM is in arithmetic, specifically when adding or subtracting fractions with different denominators. To perform the operation, you must first find a common denominator, and the most efficient choice is the least common denominator, which is the LCM of the original denominators.

Frequently Asked Questions

What is the difference between the LCM and the GCD?

Can the LCM of two numbers be one of the numbers itself?

How do you find the LCM of three or more numbers?

Is there a formula connecting LCM and GCD?