The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer divisible by all of them. LCM(4,6) = 12 because 12 is the smallest number divisible by both 4 and 6.

How is LCM related to GCD?

LCM(a,b) = |a × b| / GCD(a,b). For 4 and 6: GCD=2, LCM = 24/2 = 12. This relationship makes computing LCM via GCD fast and efficient.

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LCM Calculator

Find the Least Common Multiple of up to 10 numbers using prime factorization, with step-by-step explanation.

Calculate LCM

Enter up to 10 positive integers separated by commas

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About LCM

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the given numbers. LCM is widely used in adding and subtracting fractions, scheduling repeating events, and solving problems in number theory.

Prime Factorization Method

To find the LCM using prime factorization: factor each number into its prime components, then for each prime that appears in any factorization, take the highest power. Multiply these highest powers together to get the LCM. For example, LCM(12, 18) = LCM(2²×3, 2×3²) = 2²×3² = 36.

LCM and GCF Relationship

For any two positive integers a and b: LCM(a,b) × GCF(a,b) = a × b. This elegant relationship means you can always find the LCM if you know the GCF, and vice versa. For multiple numbers, the LCM is computed iteratively: LCM(a,b,c) = LCM(LCM(a,b),c).

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For a related calculation, use GCF Calculator to calculate the Greatest Common Factor of up to 10 numbers using the Euclidean algorithm. Alternatively, use Prime Factorization Calculator to break any integer into its prime factors. Shows exponential form, factor tree, and number of divisors.