Least Common Multiple (LCM) Calculator
Calculate the least common multiple of two or more numbers with detailed step-by-step solutions using multiple methods including prime factorization.
Enter Numbers
• Enter at least 2 positive integers
• Separate numbers with commas or spaces
• Example: 12, 18, 24
Results
Enter at least 2 numbers to calculate LCM
Methods to Find LCM
1. Listing Multiples
• List multiples of each number
• Find the smallest common multiple
• Good for small numbers
2. Prime Factorization
• Find prime factors of each number
• Take highest power of each prime
• Multiply all together
3. Using GCD Formula
• For two numbers: LCM(a,b) = (a×b)/GCD(a,b)
• Find GCD first, then calculate LCM
• Efficient for two numbers
4. Division Method
• Divide by common prime factors
• Continue until no common factors
• Multiply all divisors
Examples
Example 1: LCM of 12 and 18
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 4 × 9 = 36
Example 2: LCM of 8, 12, and 16
8 = 2³
12 = 2² × 3
16 = 2⁴
LCM = 2⁴ × 3 = 16 × 3 = 48
Frequently Asked Questions
The LCM is the smallest positive integer that is divisible by all the given numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.