LCM Calculator - Least Common Multiple

About the LCM Calculator

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the numbers. For example, the LCM of 4 and 6 is 12.

How to Find the LCM

There are several methods to find the LCM of numbers:

1. Listing Multiples

List the multiples of each number until you find the smallest common multiple.

Example: Find LCM of 4 and 6

• Multiples of 4: 4, 8, 12, 16, 20, ...
• Multiples of 6: 6, 12, 18, 24, 30, ...
• The smallest common multiple is 12.

2. Prime Factorization

Break down each number into its prime factors and multiply the highest power of each prime.

Example: Find LCM of 12 and 15

• Prime factors of 12: 2² × 3¹
• Prime factors of 15: 3¹ × 5¹
• LCM = 2² × 3¹ × 5¹ = 60

3. Using GCD (Greatest Common Divisor)

For two numbers, LCM can be calculated using the formula:

LCM(a, b) = (a × b) / GCD(a, b)

Example: Find LCM of 8 and 12

• GCD of 8 and 12 is 4
• LCM = (8 × 12) / 4 = 96 / 4 = 24

Applications of LCM

The LCM is useful in many mathematical and real-world applications:

• Finding common denominators for fractions
• Scheduling events that repeat at different intervals
• Solving problems involving gears and rotations
• Cryptography and number theory