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LCM Calculator

Find the Least Common Multiple (LCM) of two or more numbers. Free LCM calculator with steps.

Find the Least Common Multiple (LCM) of two or more numbers. Shows step-by-step work using prime factorization method.

Enter numbers separated by commas:Example: 12, 18 or 4, 6, 8

Quick examples:

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How to Use

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Enter two or more positive integers in the input field
Separate numbers with commas or spaces (e.g., "12, 18" or "4 6 8")
Click "Calculate LCM" or press Enter
View the LCM along with prime factorizations for each number

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What is LCM Calculator?

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The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the given numbers. It's also called the Lowest Common Multiple.

For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly (12 ÷ 4 = 3 and 12 ÷ 6 = 2).

The LCM is commonly used for adding and subtracting fractions with different denominators, scheduling problems, and finding common periods in cyclic events.

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Formula

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Using GCF:

LCM(a, b) = |a × b| / GCF(a, b)

Using Prime Factorization:

Take the highest power of each prime factor that appears in any of the numbers, then multiply them together.

Relationship with GCF:

LCM(a, b) × GCF(a, b) = |a × b|

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Examples

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Example 1: LCM(12, 18)

12 = 2² × 3

18 = 2 × 3²

LCM = 2² × 3² = 4 × 9 = 36

Example 2: LCM(4, 6, 8)

4 = 2²

6 = 2 × 3

8 = 2³

LCM = 2³ × 3 = 8 × 3 = 24

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FAQ

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What is the difference between LCM and GCF?expand_more

LCM (Least Common Multiple) is the smallest number that all given numbers divide into, while GCF (Greatest Common Factor) is the largest number that divides all given numbers. They are related by the formula: LCM(a,b) × GCF(a,b) = |a × b|.

What is the LCM of two prime numbers?expand_more

The LCM of two different prime numbers is simply their product. For example, LCM(3, 7) = 21, because prime numbers share no common factors other than 1.

When do I need to find the LCM?expand_more

LCM is commonly used when adding or subtracting fractions (to find a common denominator), solving scheduling problems (when events repeat at different intervals), and in various applications involving periodicity.

What if one number is a factor of another?expand_more

If one number is a factor of another, the LCM is simply the larger number. For example, LCM(4, 12) = 12, because 12 is already divisible by 4.