LCM Calculator

Find the Least Common Multiple of 2 to 5 numbers using prime factorization with a full step-by-step breakdown.

Enter 2 to 5 positive integers.

LCM Formula

LCM via Prime Factorization: Take each prime factor at its highest power across all numbers, then multiply.

LCM(a,b): LCM(a,b) = |a × b| / GCF(a,b)

Worked Example

LCM(12, 18, 30)

12 = 2² × 3

18 = 2 × 3²

30 = 2 × 3 × 5

Highest powers: 2², 3², 5

LCM = 4 × 9 × 5 = 180

Frequently Asked Questions

What is the Least Common Multiple?

The LCM of two or more integers is the smallest positive integer divisible by all of them. It is used to add fractions, find common denominators, and solve problems involving repeating cycles.

What is the difference between LCM and GCF?

The GCF (Greatest Common Factor) is the largest number that divides all given numbers. The LCM is the smallest number that all given numbers divide into. For 12 and 18: GCF = 6, LCM = 36.

How do you find LCM using prime factorization?

Factor each number into primes. For each unique prime, take the highest exponent that appears across all numbers. Multiply those prime powers together to get the LCM.

What is the relationship between LCM and GCF?

For two numbers a and b: LCM(a,b) × GCF(a,b) = a × b. This identity lets you find one if you know the other.

When is LCM used in real life?

LCM is used when adding fractions (finding common denominators), scheduling repeating events that align simultaneously (e.g., two buses with different intervals), and in music theory for rhythm patterns.