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Calculator Answers

LCM Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

An LCM calculator (Least Common Multiple) is a mathematical utility that finds the smallest positive integer that is a multiple of two or more numbers. The calculator evaluates the inputs using methods such as listing multiples, prime factorization, or the greatest common divisor formula. It outputs the least common multiple along with step-by-step math explanations for each calculation method. Students, teachers, and developers use this tool to find common denominators for fractions, solve scheduling problems, and analyze periodic events.

Enter two or more positive whole numbers. The calculator returns the least common multiple using the GCF identity, with the GCF of the list and the step by step work.

Quick Answer

Find the least common multiple (LCM) of two or more numbers. Enter your numbers to compute the smallest shared multiple and prime factorization work.

Two or more positive whole numbers, comma- or space-separated. · e.g. 12, 18, 30

The LCM (least common multiple) is the smallest whole number that every input divides evenly.

Steps

  1. lcm(12, 18) = 12 × 18 ÷ gcd(12, 18) = 36
Least common multiple

LCM

36

lcm(12, 18)

Numbers12, 18
GCF (used)6
LCM36

LCM is computed pairwise as lcm(a, b) = (a × b) ÷ gcd(a, b), then folded across the list. The result is the smallest positive integer that every input divides evenly.

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Examples

LCM of 4 and 6

= 12

LCM of 12, 18, 30

= 180

LCM of 7 and 11

= 77 (coprime → product)

How it works

For any pair of positive integers a and b, the product a × b equals gcf(a, b) × lcm(a, b). Dividing by the GCF gives the LCM. For more than two inputs, the calculator folds the pairwise rule across the list.

Pairwise · lcm(a, b) = (a × b) ÷ gcd(a, b)

More numbers · lcm(a, b, c) = lcm(lcm(a, b), c)

All inputs must be positive whole numbers.

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GCF CalculatorFind the greatest common factor of two or more whole numbers using the Euclidean algorithm, with factor lists and step by step work.

Frequently asked questions

The least common multiple (LCM) of two or more whole numbers is the smallest positive integer that every one of them divides evenly. For 4 and 6, the LCM is 12: it is the smallest number that is a multiple of both 4 and 6. It is also called the lowest common multiple.

The fastest method uses the GCF: lcm(a, b) = (a × b) ÷ gcd(a, b). For more than two numbers, fold: lcm(a, b, c) = lcm(lcm(a, b), c). This calculator runs that fold and shows the intermediate results.

GCF is the largest number that divides every input. LCM is the smallest number that every input divides into. They are connected: for any pair of positive integers a and b, a × b = gcf(a, b) × lcm(a, b). So once you know the GCF you can compute the LCM with a single division.

Adding and subtracting fractions with different denominators (the lowest common denominator is the LCM of the denominators), aligning periodic events that repeat at different intervals, and number-theory problems. Any time you need to find a common cycle or shared rhythm, the LCM is the answer.

Yes. Separate the numbers with commas or spaces, for example '12, 18, 30'. The calculator folds across the list pairwise.

LCM grows quickly when the inputs are coprime. For example, lcm(7, 11, 13, 17) = 17,017. With a handful of larger coprime numbers the result can blow past JavaScript's safe-integer range. The calculator flags this case and asks for smaller inputs.