How to find the LCM
The least common multiple is the smallest number that every one of your numbers divides into. The quickest method uses the greatest common factor:
LCM(a, b) = (a × b) ÷ GCF(a, b)
For 4 and 6, the GCF is 2, so the LCM is (4 × 6) ÷ 2 = 12. For three or more numbers, find the LCM of the first two, then combine that with the next number, and so on.
The least common denominator
To add fractions with different denominators, you need a common denominator — and the LCM of the denominators is the smallest one (the LCD). To add 1/4 + 1/6, the LCM of 4 and 6 is 12, so rewrite them as 3/12 + 2/12 = 5/12.
LCM and GCF together
For any two numbers, the least common multiple and greatest common factor multiply to the product of the numbers:
LCM(a, b) × GCF(a, b) = a × b
Frequently asked questions
What is the least common multiple (LCM)?
The LCM of two or more whole numbers is the smallest positive number that all of them divide into evenly. For 4 and 6, the multiples of 4 are 4, 8, 12, 16… and of 6 are 6, 12, 18… — the smallest they share is 12, so the LCM is 12.
How do you find the LCM?
The easiest way uses the greatest common factor: LCM(a, b) = (a × b) ÷ GCF(a, b). For 4 and 6, the GCF is 2, so the LCM is 24 ÷ 2 = 12. For more than two numbers, combine them one at a time. This calculator handles any list instantly.
What is the LCM used for?
The most common use is adding or subtracting fractions: the LCM of the denominators is the least common denominator (LCD), which lets you rewrite the fractions with a shared bottom. The LCM also answers "when do two repeating events line up again," like buses on different schedules.
What is the difference between LCM and GCF?
The LCM is the smallest number all your values divide into, while the greatest common factor (GCF) is the largest number that divides all of them. They are linked: for two numbers, GCF × LCM equals the product of the numbers. This calculator shows both.
Tip: The LCM is defined for whole numbers — decimals and fractions are rounded to the nearest whole number first.