What is the difference between LCM and GCD?

LCM (Least Common Multiple) is the smallest number divisible by all given numbers. GCD (Greatest Common Divisor) is the largest number that divides all given numbers. For 12 and 18: LCM = 36, GCD = 6.

How is LCM calculated?

The most efficient method uses the formula: LCM(a,b) = (a × b) / GCD(a,b). For multiple numbers, calculate LCM of first two, then LCM of that result with the third number, and so on.

Why is LCM important for fractions?

To add or subtract fractions with different denominators, you need a common denominator. The LCM of the denominators gives you the least common denominator (LCD), making calculations simpler.

What is the LCM of two prime numbers?

The LCM of two different prime numbers is always their product, since prime numbers have no common factors. For example, LCM(7, 11) = 77.

Least Common Multiple (LCM) Calculator

Calculate the LCM of multiple numbers instantly. Find the least common multiple using prime factorization with step-by-step explanation. Perfect for fraction operations and scheduling problems.

Numbers

Enter numbers to calculate their LCM

Least Common Multiple (LCM) Calculator Tool Introduction

A comprehensive Least Common Multiple (LCM) Calculator that finds the smallest positive number that is divisible by all given numbers. Essential for adding fractions, solving scheduling problems, and understanding number relationships.

Perfect for students learning fractions and number theory, teachers creating math problems, programmers working with cycles and periods, and anyone dealing with synchronization or scheduling tasks.

Our calculator uses efficient algorithms to compute the LCM of two or more numbers. It shows the calculation method, prime factorization, and the relationship between LCM and GCD, making it an excellent educational tool.

All calculations are performed locally in your browser for complete privacy. No data is collected or stored. Use this tool to add fractions with different denominators, solve timing problems, or understand divisibility patterns.

Least Common Multiple (LCM) Calculator User Guide

How to Use

Enter Numbers: Input two or more positive integers (comma or space separated)
Click Calculate: Get the LCM instantly
View Method: See the calculation process
Check Multiples: View common multiples

Understanding LCM

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all given numbers without remainder.

Example

Find LCM of 12 and 18:

Multiples of 12: 12, 24, 36, 48, 60, 72...
Multiples of 18: 18, 36, 54, 72, 90...
Common multiples: 36, 72, 108...
LCM = 36 (the smallest)

Using Prime Factorization

LCM(12, 18):

12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 4 × 9 = 36

LCM and GCD Relationship

For two numbers a and b:

LCM(a, b) × GCD(a, b) = a × b

Key Features

Calculate LCM of 2 or more numbers
Show calculation method
Display prime factorization
Show LCM-GCD relationship
List common multiples
Fast computation for large numbers

Frequently Asked Questions

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