Guide
What Is the Least Common Multiple (LCM)?
The least common multiple is what lets you add and subtract fractions with unlike denominators.
The least common multiple is what lets you add and subtract fractions with unlike denominators.
What the LCM is
The least common multiple (LCM) of two or more numbers is the smallest number that all of them divide into evenly. The LCM of 4 and 6 is 12.
Finding it by listing multiples
List multiples of each number until you find the smallest shared one. Multiples of 4: 4, 8, 12, 16. Multiples of 6: 6, 12, 18. The smallest shared multiple is 12.
Finding it by prime factorization
Take the highest power of each prime that appears. 4 = 2 x 2 and 6 = 2 x 3; take 2 x 2 (from 4) and 3 (from 6) to get 12.
LCM vs LCD
When the numbers are the denominators of fractions, the LCM is exactly the least common denominator (LCD). Finding the LCM of the denominators is how you add or subtract unlike fractions.
Related tools & guides
Frequently asked
What is the least common multiple?
The smallest number that two or more numbers all divide into evenly. The LCM of 4 and 6 is 12.
How do you find the LCM?
List the multiples of each number and pick the smallest they share, or use prime factorization taking the highest power of each prime.
Is the LCM the same as the least common denominator?
When the numbers are fraction denominators, yes — the LCM of the denominators is the least common denominator.