There is more than one route to the same LCM. Below are the four standard methods — each with a worked example — so you can match the approach your class, exam or workflow expects. Want the answer instantly? Use the calculator.
Break each number into its prime factors, then multiply the highest power of every prime that appears in any number.
LCM(12, 18): 12 = 2²×3, 18 = 2×3². Highest powers: 2² and 3² → 2²×3² = 36.
Best for: understanding why the LCM works and handling three or more numbers reliably.
The fastest method for two numbers uses the Greatest Common Factor:
LCM(a, b) = (a × b) ÷ GCF(a, b)LCM(12, 18): GCF = 6, so (12 × 18) ÷ 6 = 36. For more than two numbers, apply it pairwise.
Best for: speed and mental math with two values.
Write out the multiples of each number and find the smallest value they share.
4 → 4, 8, 12 · 6 → 6, 12. First shared multiple = 12.
Best for: small numbers and visual learners. It becomes slow for large values.
Stack the numbers and divide the whole row by a common prime, repeating until every value is 1. Multiply all the divisors.
LCM(8, 9, 21): ÷2, ÷2, ÷2, ÷3, ÷3, ÷7 → 2³×3²×7 = 504.
Best for: three or more numbers in a compact, exam-friendly layout.
The LCM and GCF are two sides of the same coin. For any two positive integers:
So if you know one, you can always derive the other. This is why the GCF formula is the quickest route to an LCM.
Switch methods inside the calculator and compare the working side by side.
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