Math & Algebra Tool

LCM Calculator

Find the Least Common Multiple (LCM) of two or more numbers.

Separate values with commas or spaces.

Σ The Formula

LCM(a,b) = (a × b) / GCF(a,b)

Real World Examples

Simple LCM
LCM(4, 6) = 12
Three Numbers
LCM(12, 15, 20) = 60
Adding Fractions
1/4 + 1/6: LCD = LCM(4,6) = 12, so 3/12 + 2/12 = 5/12
Scheduling
Events every 6 and 8 days: LCM(6,8) = 24 days until both occur

# About This Calculator

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all the given numbers. It's the "smallest common multiple" that all numbers share. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6.

LCM is essential for adding or subtracting fractions with different denominators (the LCM becomes the Least Common Denominator or LCD), solving scheduling problems (when events repeat at different intervals), and understanding number patterns. It's also used in music theory, gear ratios, and synchronized systems.

To find LCM, use prime factorization: break each number into prime factors, then take the highest power of each prime that appears. For example, 12=2²×3 and 18=2×3², so LCM=2²×3²=36. Alternatively, use the formula: LCM(a,b) = (a×b)/GCF(a,b).

This calculator handles multiple numbers simultaneously, shows prime factorization steps, and identifies the LCM efficiently. Perfect for homework, fraction operations, or any problem requiring the least common multiple.

How To Use

  1. Enter numbers separated by commas or spaces (e.g., "12, 15, 20").
  2. Click Calculate LCM.
  3. See the LCM result and the prime factorization method used to find it.

Frequently Asked Questions

What is LCM?+

LCM stands for Least Common Multiple. It is the smallest positive integer that is divisible by all given numbers. For example, LCM(4,6)=12 because 12 is the smallest number that both 4 and 6 divide into evenly.

How do I use LCM to add fractions?+

Find the LCM of the denominators (this is the LCD - Least Common Denominator). Convert each fraction to have this denominator, then add. For 1/4 + 1/6: LCM(4,6)=12, so 3/12 + 2/12 = 5/12.

What's the relationship between LCM and GCF?+

For two numbers a and b: LCM(a,b) × GCF(a,b) = a × b. This means if you know one, you can find the other. For example, LCM(12,18)=36, GCF(12,18)=6, and 36×6 = 12×18 = 216.

Can LCM be smaller than one of the numbers?+

No! The LCM must be at least as large as the biggest number in the set. In fact, if one number is a multiple of all others, it IS the LCM. For example, LCM(3, 6, 12) = 12.

What's the LCM of two prime numbers?+

Always their product! Prime numbers share no common factors, so LCM(p,q) = p×q. For example, LCM(7,11) = 77, LCM(13,17) = 221. This is why adding fractions with prime denominators creates large denominators.

Is LCM Calculator free to use?+

Yes, LCM Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all the given numbers. It's the "smallest common multiple" that all numbers share. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6.

LCM is essential for adding or subtracting fractions with different denominators (the LCM becomes the Least Common Denominator or LCD), solving scheduling problems (when events repeat at different intervals), and understanding number patterns. It's also used in music theory, gear ratios, and synchronized systems.

To find LCM, use prime factorization: break each number into prime factors, then take the highest power of each prime that appears. For example, 12=2²×3 and 18=2×3², so LCM=2²×3²=36. Alternatively, use the formula: LCM(a,b) = (a×b)/GCF(a,b).

This calculator handles multiple numbers simultaneously, shows prime factorization steps, and identifies the LCM efficiently. Perfect for homework, fraction operations, or any problem requiring the least common multiple.

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