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The quickest way to find the LCM of two numbers is the formula LCM(a, b) = (a × b) ÷ GCF(a, b). But there are four reliable methods, and the best one depends on the numbers and what your class expects.
This guide walks through all four — prime factorization, the GCF formula, listing multiples and the division ladder — with worked examples for each, so you can pick the fastest route every time.
What is the Least Common Multiple?
The Least Common Multiple (LCM) of two or more whole numbers is the smallest positive number that every input divides into evenly. For example, the LCM of 4 and 6 is 12, because 12 is the first value that appears in both the 4-times table (4, 8, 12…) and the 6-times table (6, 12…).
The LCM is essential for adding fractions, solving scheduling problems and reducing ratios. You can compute any example instantly with the LCM Calculator.
Method 1: Prime factorization
Break each number into prime factors, then multiply the highest power of every prime that appears.
Example — LCM(12, 18): 12 = 2² × 3 and 18 = 2 × 3². Take 2² (from 12) and 3² (from 18): LCM = 2² × 3² = 36. This method scales beautifully to three or more numbers.
Method 2: The GCF formula (fastest for two numbers)
Use LCM(a, b) = (a × b) ÷ GCF(a, b). For 12 and 18, the GCF is 6, so LCM = (12 × 18) ÷ 6 = 36. Find the GCF first with the GCD Calculator.
Method 3: Listing multiples
Write out the multiples of each number and circle the first one they share. For 4 and 6: 4, 8, 12… and 6, 12… The first common multiple is 12. This is intuitive for small numbers but slow for large ones.
Method 4: The division (ladder) method
Stack the numbers and divide the row by common primes until every value is 1. Multiply the divisors down the side to get the LCM. This is a favourite in many school curricula because it handles several numbers at once.
Which method should you use?
- Two numbers, quick answer: the GCF formula.
- Three or more numbers: prime factorization or the division ladder.
- Small numbers / learning: listing multiples for intuition.
Key takeaways
- The LCM is the smallest number all inputs divide into.
- The fastest two-number method is LCM = (a × b) ÷ GCF(a, b).
- Prime factorization scales best for three or more numbers.
- LCM × GCF = the product of the two numbers.
Frequently asked questions
What is the easiest way to find the LCM?
For two numbers, use the GCF formula: LCM(a, b) = (a × b) ÷ GCF(a, b). For several numbers, prime factorization is usually clearest.
How do you find the LCM of three numbers?
Use prime factorization (take the highest power of each prime across all three) or the division ladder method, which handles the whole set at once.
Is the LCM ever smaller than the largest number?
No. The LCM is always greater than or equal to the largest input, because it must be a multiple of it.
The LCM Calculator Team
Math educators and engineers building free, accurate calculators with step-by-step solutions, visual diagrams and AI insights.
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