Factor Calculator

LCM Calculator

Find the smallest positive integer that is a multiple of two numbers.

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What is the Least Common Multiple?

The Least Common Multiple (LCM) is the smallest positive integer that is a multiple of 2 or more numbers. The LCM of 4 and 6 is 12 because 12 is the smallest number that both 4 and 6 divide into evenly. The LCM calculator computes this using the formula LCM(a, b) = (a × b) / GCF(a, b).

LCM is used in 3 primary areas: adding and subtracting fractions with different denominators (finding the Least Common Denominator), scheduling recurring events, and solving problems in number theory. The relationship between LCM and GCF — LCM × GCF = product of the 2 numbers — makes computation efficient.

How to Calculate LCM

The number line below shows multiples of both numbers. The first point where they overlap is the LCM.

Multiples Number Line

Multiples of 4

4812162024

Multiples of 6

6121824

First common multiple → LCM(4, 6) = 12

Formula: (4 × 6) / GCF(4, 6) = 24 / 2 = 12

LCM Worked Examples

LCM(4, 6)= 12

Multiples of 4: 4, 8, 12… Multiples of 6: 6, 12… The first common multiple is 12. Using the formula: LCM = (4 × 6) / GCF(4,6) = 24 / 2 = 12.

LCM(12, 18)= 36
LCM(15, 20)= 60
LCM(8, 14)= 56

Frequently Asked Questions

LCM and GCF are connected by the formula: LCM(a, b) × GCF(a, b) = a × b. This means you can calculate LCM from GCF: LCM = (a × b) / GCF. For 12 and 18: GCF = 6, so LCM = (12 × 18) / 6 = 36. This relationship holds for any 2 positive integers and makes the LCM calculator efficient — compute GCF first using the Euclidean algorithm, then derive LCM in one step.