LCM and HCF Calculator

The LCM (Least Common Multiple) of two numbers is the smallest number that is divisible by both. The HCF (Highest Common Factor), also called GCD (Greatest Common Divisor), is the largest number that divides both without a remainder.

Example: LCM(4, 6) = 12, HCF(4, 6) = 2.

These are fundamental concepts used in fractions (finding common denominators), scheduling problems, and number theory.

1. Prime Factorisation Method:
   • Find prime factors of each number
   • HCF = product of common prime factors (lowest power)
   • LCM = product of all prime factors (highest power)
2. Euclidean Algorithm (for HCF):
   • HCF(a, b) = HCF(b, a mod b) until remainder = 0
   • LCM(a, b) = (a × b) / HCF(a, b)

To find LCM/HCF of three numbers (a, b, c):

• HCF(a,b,c) = HCF(HCF(a,b), c)
• LCM(a,b,c) = LCM(LCM(a,b), c)

Example: LCM(4, 6, 10):
LCM(4,6) = 12, then LCM(12,10) = 60.
HCF(4,6) = 2, then HCF(2,10) = 2.

Enter the third number in the optional "Third Number" field above to calculate instantly.

• Fractions: Finding the LCD (Lowest Common Denominator) to add/subtract fractions
• Scheduling: When do two events next occur together? (LCM of their periods)
• Tiling: Largest tile size that fits a room perfectly (HCF of room dimensions)
• Distribution: Splitting items equally into groups (HCF)
• Maths Olympiad: LCM/HCF problems in competitive exams