What is the Least Common Multiple?
The Least Common Multiple (LCM) of two or more whole numbers is the smallest positive integer that is divisible by all of them. It is sometimes called the lowest common multiple or smallest common multiple. For instance, the LCM of 4 and 6 is 12 — the first number that appears in both times tables.
How is the LCM calculated?
There are four standard approaches, all covered on the methods page:
- Prime factorization — multiply the highest power of each prime.
- GCF formula —
LCM(a,b) = (a×b) ÷ GCF(a,b). - Listing multiples — find the first shared multiple.
- Division ladder — divide by common primes until all values are 1.
Why does the LCM matter?
The LCM turns up far beyond the classroom. The most common use is adding and comparing fractions, where the lowest common denominator is simply the LCM of the denominators. It also appears in scheduling, gear and signal timing, and number theory.
Adding fractions example
To add 1/6 + 1/8, the LCD is LCM(6, 8) = 24. Rewrite as 4/24 + 3/24 = 7/24.
LCM vs GCF
The GCF (Greatest Common Factor) is the largest number that divides all inputs, while the LCM is the smallest number they all divide into. They satisfy LCM(a,b) × GCF(a,b) = a × b.