Please provide numbers separated by a comma "," and click the "Calculate" button to find the LCM.
In elementary number theory and arithmetic, the Least Common Multiple (denoted as LCM, or lowest common multiple / smallest common multiple) of two or more non-zero integers a and b is the smallest positive integer that is divisible by both a and b without leaving a remainder.
For instance, consider the integers 4 and 6:
The common multiples are 12, 24, 36, ... and the least among them is 12. Thus, LCM(4, 6) = 12.
Break each integer down into powers of its prime factors. The LCM is the product of the highest power of every prime factor appearing across any number:
Using the Euclidean algorithm, compute the GCD of the numbers. The product of two numbers divided by their GCD gives their LCM:
Place the numbers in an upside-down division bracket. Repeatedly divide by prime numbers that divide at least two numbers. Multiply all divisors on the left by the numbers in the final bottom row.
List the consecutive multiples of each number (a, 2a, 3a, 4a, ...) until the first common integer appears in all lists. Ideal for mental math with small numbers.
Finding the Least Common Denominator (LCD) when adding or subtracting fractions with unlike denominators is identical to finding the LCM of the denominators.
Determining when multiple periodic events will occur simultaneously (e.g. traffic lights cycling every 45s and 60s, or buses arriving at a shared stop).
Mechanical engineers calculate how many tooth revolutions must occur before identical teeth on meshing gears touch again using the LCM of their tooth counts.
Because two distinct prime numbers share no common factors other than 1 (they are coprime, GCD = 1), their LCM is simply their direct product: LCM(p, q) = p × q. (e.g. LCM(7, 11) = 77).
By standard mathematical convention, LCM(a, 0) = 0, because 0 is a multiple of every integer (0 = k × 0).
For any two positive integers a and b, the product of their LCM and GCF equals the product of the two numbers: LCM(a, b) × GCF(a, b) = a × b.