Key Relationships
How to Use
Enter 2 to 4 positive integers. Numbers 3 and 4 are optional.
Click Calculate to find HCF and LCM instantly.
See the prime factorization of each number to understand the method.
Frequently Asked Questions
For two numbers a and b: HCF(a,b) × LCM(a,b) = a × b. This is a key formula used in SSC and IBPS exams to find LCM when HCF is given, or vice versa.
12 = 2² × 3; 18 = 2 × 3². Common factors: 2¹ × 3¹. HCF = 6. LCM = 2² × 3² = 36. Verify: 6 × 36 = 216 = 12 × 18 ✓
LCM is used in: bells ringing at intervals, pipes filling tanks together, runners meeting again at start, and finding the smallest number divisible by given values. HCF is used in: dividing into equal groups, tiling floors, and rope-cutting problems. Memorise this distinction — exam questions are designed to test whether you pick HCF or LCM.
Find LCM(6, 8, 12). 6 = 2 × 3; 8 = 2³; 12 = 2² × 3. LCM = 2³ × 3 = 24 minutes. They will all ring together again after every 24 minutes. This is one of the most common LCM application types in SSC CGL and IBPS PO exams.
When remainders are equal, subtract the remainder from each number first: 70−5=65, 80−5=75, 105−5=100. The required number = HCF(65, 75, 100). 65 = 5×13; 75 = 3×5²; 100 = 2²×5². HCF = 5. Rule: if same remainder, subtract it and find HCF. If different remainders, subtract each remainder from its number and find HCF of the differences.