LCM Calculator

The LCM Calculator (Least Common Multiple Calculator) finds the smallest positive integer that is exactly divisible by two or more given numbers. LCM is a fundamental concept in mathematics, taught from primary school through competitive exam preparation. It is essential for adding and subtracting fractions with different denominators, solving word problems involving cycles and periods, and mastering competitive exam aptitude sections.

This calculator computes LCM instantly using the Euclidean algorithm and also shows the HCF (Highest Common Factor) as a bonus result.

Where LCM Is Used

- Adding fractions: To add 1/4 + 1/6, you need the LCM of 4 and 6 (which is 12) as the common denominator: 3/12 + 2/12 = 5/12.

- Synchronization problems: If two events happen every 4 days and 6 days respectively, they next coincide after LCM(4,6) = 12 days. This type of problem appears in every major competitive exam in India.

- Tiling problems: LCM helps find the smallest square tile that can cover a rectangular floor without cutting.

- Clock problems: LCM is used in clock problems — when will two clock hands meet again?

- School exams: LCM is a core chapter in Class 5–8 mathematics across all Indian school boards (CBSE, ICSE, state boards).

LCM and HCF Relationship

A fundamental property: LCM(a,b) × HCF(a,b) = a × b. This relationship is frequently tested in competitive exams. Knowing one value, you can always find the other. This calculator uses HCF to compute LCM efficiently: LCM(a,b) = (a × b) / HCF(a,b).

1. Enter Number 1: Type the first positive integer.

2. Enter Number 2: Type the second positive integer.

3. View Results: The calculator instantly shows the LCM and also displays the HCF as a bonus.