Least common multiple and GCF of two or more whole numbers, with free step-by-step work
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This LCM calculator finds the least common multiple and the greatest common factor of two or more positive integers. Type the numbers in one box, separated by commas or spaces. 12, 18 and 12 18 are the same problem. The page shows both answers at once, plus the prime factorization of each number when the numbers are small enough to factor here.
Prime factorization writes each number as primes with exponents, then takes the highest power of every prime for the LCM and the lowest power that divides every number for the GCF. The ladder, or cake method, divides by a prime that splits at least two numbers and stops when the bottom row shares no prime; the LCM is the product of the divisors and that bottom row. The division table keeps going until every entry is 1, and the LCM is the product of the left column. Listing multiples walks the multiples of the largest number until one is divisible by the others. That list stops after 40 multiples and still reports the exact LCM. LCM via GCF uses Euclid's algorithm, then LCM(a, b) = (a ÷ GCF) × b, one pair at a time.
The least common denominator of two fractions is the LCM of their denominators. 1/12 + 1/18 needs LCD 36. The fraction calculator does that addition, including the LCD step, when you type the fractions there.
Zero, negatives, and decimals are rejected. One number is not enough, and more than 20 numbers is refused. Each number can have up to 100 digits. The arithmetic uses whole-number math, so values past the usual safe integer limit stay exact. Prime tables are shown up to 1,000,000,000,000. Larger numbers still get an exact LCM and GCF, with the Euclid steps on the LCM via GCF tab. The page runs in the browser. There is no account, and the numbers are not uploaded.
Related on UtilGenie: Fraction Calculator, Percentage Calculator, Grade Calculator, Unit Converter.
Find the least common multiple and greatest common factor of two or more whole numbers, then read the steps.
Open the LCM calculator.
Enter two or more positive integers, separated by commas or spaces.
Read the least common multiple and the greatest common factor.
Open a method tab: prime factorization, the ladder, the division table, listing multiples, or LCM via GCF.
Copy a result or the share link. Nothing is saved to an account.
The least common multiple is the smallest positive integer that each of your numbers divides evenly. Multiples of 4 include 4, 8, 12, and 16. Multiples of 6 include 6, 12, and 18. The first shared number is 12, so the LCM of 4 and 6 is 12.
Use the same methods as for two numbers. Prime factorization keeps the highest power of every prime. The ladder and the division table multiply the divisors (and, for the ladder, the bottom row). You can also take the LCM of the first pair, then the LCM of that result and the third number. LCM(4, 6, 8) is 24, and the GCF is 2.
The LCM is the smallest shared multiple. The GCF, also called the GCD or greatest common divisor, is the largest positive integer that divides every number. For 12 and 18 the LCM is 36 and the GCF is 6. For two numbers, LCM(a, b) times GCF(a, b) equals a times b.
The LCM of 12 and 18 is 36. Their GCF is 6. In primes, 12 = 2^2 × 3 and 18 = 2 × 3^2, so the LCM is 2^2 × 3^2 = 36. The ladder divides by 2 and then by 3, leaving 2 and 3 on the bottom row, and 2 × 3 × 2 × 3 = 36.
When denominators differ, the least common denominator is the LCM of the denominators. To add 1/12 and 1/18, the LCD is 36, so the sum is 3/36 + 2/36 = 5/36. The fraction calculator uses that step when it adds or subtracts.
Yes. It runs in your browser, needs no account, and does not upload the numbers. A share link only stores the calculation in the URL you copy.
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Separate positive integers with commas or spaces. Decimals, zero, and negative numbers are rejected.
Least common multiple
36
Greatest common factor
6
Use 36 as the LCD in the fraction calculator.
