Key Relationships
HCF × LCM (two numbers)
HCF(a,b) × LCM(a,b) = a × b
LCM from HCF
LCM = (a × b) ÷ HCF(a,b)
HCF Method
Product of COMMON prime factors (lowest power)
LCM Method
Product of ALL prime factors (highest power)
How to Use
1
Enter Numbers
Enter 2 to 4 positive integers. Numbers 3 and 4 are optional.
2
Calculate
Click Calculate to find HCF and LCM instantly.
3
View Factorization
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 problems involving: bells ringing at intervals, pipes filling tanks together, runners meeting again at the start, and finding the smallest number divisible by given numbers. HCF is used in dividing into equal groups, tiling problems, and rope-cutting problems.