What Is the Least Common Multiple?
Definition
Least Common Multiple: The smallest positive whole number that is a multiple of each of two or more whole numbers, also called the lowest common multiple. The LCM of 24 and 30 is 120.
The least common multiple (LCM), also called the lowest common multiple, is the smallest positive whole number that is a multiple of each of two or more whole numbers. The LCM of 24 and 30 is 120. You use it to find a common denominator when you add or subtract fractions, and to find when repeating events first meet.
Where it appears in the formulas
LCM = product of all prime factors, each with its highest power. Since 24 = 2³ × 3 and 30 = 2 × 3 × 5, LCM(24, 30) = 2³ × 3 × 5 = 120. The GCD and LCM calculator finds it this way for up to 10 numbers. For two numbers, a × b = GCD(a, b) × LCM(a, b) also holds.
How it differs from the GCD
The GCD is the largest number that divides all the numbers; the LCM is the smallest number that all of them divide. With fractions, the GCD simplifies and the LCM gives the common denominator: to add 1/4 and 1/6, use LCM(4, 6) = 12 as the denominator.