LCM & HCF Calculator

Frequently Asked Questions

• What is LCM (Lowest Common Multiple)?+
  The LCM of two or more numbers is the smallest number divisible by all of them. Example: LCM of 4 and 6 is 12 — the smallest number both 4 and 6 divide into evenly. LCM is used when adding fractions with different denominators and in scheduling problems (when will two events next coincide?).
• What is HCF (Highest Common Factor)?+
  The HCF (also called GCD — Greatest Common Divisor) is the largest number that divides all the given numbers without a remainder. Example: HCF of 12 and 18 is 6 — the largest number dividing both. HCF is used in simplifying fractions and dividing things into the largest equal groups.
• What is the relationship between LCM and HCF?+
  For any two positive integers a and b:
  LCM(a,b) × HCF(a,b) = a × b
  
  Example: LCM(12,18) = 36, HCF(12,18) = 6, and 36 × 6 = 216 = 12 × 18. ✓
  This relationship holds for two numbers only.
• How do you find LCM and HCF using prime factorisation?+
  Break each number into prime factors.
  For HCF: take the lowest power of each prime that appears in ALL numbers.
  For LCM: take the highest power of each prime that appears in ANY number.
  
  Example: 12 = 2² × 3, 18 = 2 × 3²
  HCF = 2¹ × 3¹ = 6 · LCM = 2² × 3² = 36
• What is Euclid's algorithm for HCF?+
  Euclid's algorithm: HCF(a, b) = HCF(b, a mod b), repeated until the remainder is 0.
  Example: HCF(48, 18) → HCF(18, 12) → HCF(12, 6) → HCF(6, 0) = 6
  This is the fastest method for large numbers and is what all computers use internally.