Least Common Multiple (LCM) Calculator

Find the Smallest Common Multiple

The Least Common Multiple (LCM) is the smallest positive integer that is a multiple of two or more numbers. This calculator finds the LCM for a given set of numbers, which is particularly useful when adding or subtracting fractions with different denominators and in various number theory problems.

The LCM Formula Explained

The easiest way to calculate the LCM of two numbers (a and b) is to use their Greatest Common Factor (GCF): LCM(a, b) = (a * b) / GCF(a, b) To find the LCM of more than two numbers, you find the LCM of the first two, then find the LCM of that result and the third number, and so on.

How to Use the Calculator

1. Enter Numbers: Input two or more whole numbers, separated by commas.
2. Calculate LCM: The tool will compute and display the least common multiple.

Real-World Example

You want to find the LCM of 12 and 15.

1. First, find the GCF of 12 and 15. The GCF is 3.
2. Calculation: LCM(12, 15) = (12 * 15) / GCF(12, 15) = 180 / 3 = 60 The LCM is 60.

Frequently Asked Questions (FAQ)

• What is the LCM used for? Its primary use is in fraction arithmetic. To add 1/12 + 1/15, you need to find a common denominator. The LCM (60) is the 'least common denominator'. You would convert the fractions to 5/60 + 4/60 = 9/60.
• Can I use negative numbers? The LCM is defined for positive integers. The calculator will use the absolute values of any negative numbers you enter.
• Is there a relationship between GCF and LCM? Yes, for any two positive integers a and b, it is always true that a * b = GCF(a, b) * LCM(a, b).