Lowest Common Multiple (LCM) Calculator

The Lowest Common Multiple (LCM) is the smallest positive number that is a multiple of all the numbers in a set.

Enter two or more positive numbers, separated by commas or spaces.

What is the Lowest Common Multiple (LCM)?

The Lowest Common Multiple, or LCM, is the smallest positive whole number that is a multiple of two or more other numbers. A "multiple" is the result of multiplying a number by an integer.

For example, let's find the LCM of 4 and 6:

  • The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
  • The multiples of 6 are: 6, 12, 18, 24, 30, ...

The "common multiples" are 12, 24, 36, and so on. The "lowest" of these common multiples is 12. Therefore, the LCM of 4 and 6 is 12.

LCM and GCF: What's the Relationship?

The LCM is closely related to the GCF (Greatest Common Factor). There is a very useful formula that connects them:

LCM(a, b) = (|a × b|) / GCF(a, b)

In words: "The LCM of two numbers is their product divided by their Greatest Common Factor." This is the fastest way to calculate the LCM and is the primary method this calculator uses.

How to Use This LCM Calculator

This tool is designed to be a fast and effective learning aid. Here’s how to use it:

  1. Enter Numbers: In the input box, type the numbers you want to find the LCM for. You must enter at least two numbers, separated by a comma (,) or a space.
  2. Calculate LCM: Click the "Calculate LCM" button.
  3. Review the Steps: The calculator not only gives you the answer but also shows you how to find it yourself. It provides detailed, step-by-step breakdowns using all three common methods:
    • Listing Multiples: The simplest method, perfect for small numbers.
    • Prime Factorization: A very common method taught in schools.
    • GCF Formula: The fastest and most efficient method, especially for large numbers.

LCM Solved Examples

Example 1: Find the LCM of two numbers (9 and 12)

We can use the "Listing Multiples" method, which is great for visual learners.

  1. List multiples of 9: 9, 18, 27, 36, 45, 54, ...
  2. List multiples of 12: 12, 24, 36, 48, 60, ...
  3. Find the lowest common multiple:
    The first number that appears in both lists is 36.

Result: The LCM of 9 and 12 is 36.

Example 2: Find the LCM of three numbers (4, 6, and 8)

Let's use the "Prime Factorization" method for this one.

  1. Find the prime factors of 4: 4 = 2 × 2
  2. Find the prime factors of 6: 6 = 2 × 3
  3. Find the prime factors of 8: 8 = 2 × 2 × 2
  4. Find the highest power of all primes:
    Look for the prime factors that appear in *any* list and take the *highest* number of occurrences.
    • The highest power of 2 is 2 × 2 × 2 (from the 8).
    • The highest power of 3 is 3 (from the 6).
  5. Multiply these highest powers together: (2 × 2 × 2) × 3 = 8 × 3 = 24

Result: The LCM of 4, 6, and 8 is 24.

Frequently Asked Questions

What is the LCM (Lowest Common Multiple)?

The Lowest Common Multiple (LCM) is the smallest positive number that is a multiple of all the numbers in a set. For example, the LCM of 4 and 6 is 12.

What is the least common multiple of 4 and 9?

The least common multiple of 4 and 9 is 36.

What is the least common multiple of 7 and 8?

The least common multiple of 7 and 8 is 56.

What is the least common multiple of 3 and 5?

The least common multiple of 3 and 5 is 15.

What is the relationship between LCM and GCF?

The LCM and GCF (Greatest Common Factor) are closely related. For two numbers 'a' and 'b', the formula is: LCM(a, b) = (a * b) / GCF(a, b).

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