LCM Calculator
Use this calculator to find the Least Common Multiple (LCM) of two or more numbers. Enter numbers separated by commas and click Calculate. Step-by-step solutions using all three methods are shown below.
Please enter valid positive integers separated by commas.
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Least Common Multiple (LCM)
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Note: The LCM of two or more integers is the smallest positive integer divisible by all of them. LCM is widely used in fraction arithmetic (finding common denominators), scheduling problems, and number theory.
What is the Least Common Multiple (LCM)?
In mathematics, the Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of them. It is commonly denoted as LCM(a, b).
Prime Factorization Method
Break each number into its prime factors. The LCM is the product of the highest power of every prime that appears in any factorization.
EX: Find LCM(21, 14, 38)
21 = 3 x 7
14 = 2 x 7
38 = 2 x 19
LCM = 3^1 x 7^1 x 2^1 x 19^1 = 798
GCF / GCD Method
Using the Greatest Common Factor: LCM(a, b) = (a x b) / GCF(a, b). For more than two numbers, apply the formula iteratively.
EX: LCM(14, 38)
GCF(14, 38) = 2
LCM(14, 38) = (14 x 38) / 2 = 266
LCM(266, 21)
GCF(266, 21) = 7
LCM(266, 21) = (266 x 21) / 7 = 798
Listing Multiples (Brute Force)
List multiples of each number until a common multiple is found. The first (smallest) match is the LCM.
EX: Find LCM(18, 26)
18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234
26: 52, 78, 104, 130, 156, 182, 208, 234
LCM(18, 26) = 234