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LCM Calculator

Find the least common multiple (LCM) of two or more positive integers, with GCD and prime-factorization steps.

ExampleSample values — edit any field to see your result.

Separate positive integers with commas. At least two numbers are required.

Results update as you type.

LCM

LCM(330, 75, 450, 225) = 4950

Estimated result

Least common multiple
4950
Greatest common divisor
15

Calculation steps

Worked solution
Prime factorization of the numbers:
330 = 2 × 3 × 5 × 11
75 = 3 × 5 × 5
450 = 2 × 3 × 3 × 5 × 5
225 = 3 × 3 × 5 × 5
LCM(330, 75, 450, 225)
= 2 × 3 × 3 × 5 × 5 × 11
= 4950
GCD(330, 75, 450, 225) = 15
LCMLCM(330, 75, 450, 225) = 4950

Enter two or more positive integers, separated by commas, to find their least common multiple (LCM) — also called the lowest common multiple — with GCD and prime-factorization steps.

Formula

The LCM is the smallest positive integer divisible by every listed number.

Prime factorization. Factor each integer, keep the highest power of each prime, and multiply:

LCM(21, 14, 38)
21 = 3 × 7
14 = 2 × 7
38 = 2 × 19
LCM = 2 × 3 × 7 × 19 = 798

Greatest common divisor. For two positive integers a and b,

LCM(a, b) = (a × b) / GCD(a, b)

Extra integers fold in the same way: LCM(a, b, c) = LCM(LCM(a, b), c).

LCM and GCF are inverses for two numbers: LCM(a, b) × GCF(a, b) = a × b. Use the GCF calculator when you want the greatest common factor.

Examples

Default list 330, 75, 450, 225

Prime factors: 330 = 2 × 3 × 5 × 11, 75 = 3 × 5 × 5, 450 = 2 × 3 × 3 × 5 × 5, and 225 = 3 × 3 × 5 × 5. Highest powers are 2, 3², 5², and 11, so the LCM is 4950. The GCD of the same list is 15.

Page example 18, 26

GCD(18, 26) = 2, so LCM = (18 × 26) / 2 = 234. Prime factors 2 × 3 × 3 × 13 give the same result.

Page example 21, 14, 38

LCM(14, 38) = 266, then LCM(266, 21) = 798. The primes 2, 3, 7, and 19 multiply to the same value.

Frequently asked questions

What is the least common multiple (LCM)?
The LCM (also called the lowest common multiple) of two or more integers is the smallest positive integer that is divisible by each of them. For example, LCM(18, 26) = 234.
How should I enter the numbers?
Type or paste at least two positive integers separated by commas, such as 330, 75, 450, 225. Spaces around commas and new lines are fine. Trailing commas and blank slots between numbers are ignored. Zero, negatives, decimals that are not whole numbers, and non-numeric text are rejected.
How do you find the LCM by prime factorization?
Factor each integer into primes, then multiply the highest power of every prime that appears. For 21 = 3×7, 14 = 2×7, and 38 = 2×19, the LCM is 2×3×7×19 = 798.
How do you find the LCM using the GCD?
For two positive integers, LCM(a, b) = (a × b) / GCD(a, b). For more than two numbers, fold pairwise: find LCM(a, b) first, then take the LCM of that result and the next number. LCM(14, 38) = 266, then LCM(266, 21) = 798.
What is the difference between LCM and GCF?
The LCM is the smallest shared multiple; the GCF (or GCD) is the largest shared factor. They are related by LCM(a, b) × GCF(a, b) = a × b. Use the GCF calculator when you want the greatest common factor instead.

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