LCM Calculator — Least Common Multiple of 2-5 Numbers
Calculate the Least Common Multiple (LCM) of up to 5 numbers using prime factorization. Full step-by-step solution shown.
Examples:
—
LCM
Prime Factorization Method
How LCM Works
The prime factorization method: factor each number into primes, then multiply each prime at its highest power across all numbers.
For LCM(12, 18, 24): 12 = 2²×3, 18 = 2×3², 24 = 2³×3. LCM = 2³×3² = 8×9 = 72
Frequently Asked Questions
What is the LCM (Least Common Multiple)?
The Least Common Multiple of two or more integers is the smallest positive integer that is divisible by all of them. For example, LCM(4, 6) = 12 because 12 is the smallest number that is both a multiple of 4 and a multiple of 6.
How is LCM calculated using prime factorization?
Find the prime factorization of each number. Take each prime factor at its highest power. Multiply these together. For example, LCM(12, 18): 12 = 2²×3, 18 = 2×3². LCM = 2²×3² = 4×9 = 36.
What is the relationship between LCM and GCD?
For any two positive integers a and b: LCM(a, b) = (a × b) / GCD(a, b). This is an efficient way to compute LCM using the Euclidean algorithm for GCD.
When is LCM used in real life?
LCM is used to add fractions (finding a common denominator), to determine when periodic events will coincide (e.g., two traffic lights that cycle at different intervals), and in scheduling problems.
Can LCM be found for more than two numbers?
Yes. For multiple numbers, calculate LCM iteratively: LCM(a,b,c) = LCM(LCM(a,b),c). This calculator supports up to 5 numbers.