HCF LCM Calculator
Find the HCF/GCD and LCM of two or three numbers with steps
Enter Your Numbers
Whole numbers from 1 to 1,000,000.
Your Result
HCF / GCD
6
LCM
72
of 12, 18, 24
Steps (Euclidean algorithm)
gcd(12, 18):
12 ÷ 18 = 0 remainder 12
18 ÷ 12 = 1 remainder 6
12 ÷ 6 = 2 remainder 0
→ GCD = 6
gcd(6, 24):
6 ÷ 24 = 0 remainder 6
24 ÷ 6 = 4 remainder 0
→ GCD = 6
LCM(12, 18, 24) = 72
About this Tool
The HCF (Highest Common Factor, also called GCD) is the largest number dividing all inputs, found here with the Euclidean algorithm of repeated division. The LCM (Least Common Multiple) is the smallest number all inputs divide into evenly, computed as (a × b) ÷ GCD. This tool handles two or three whole numbers and shows every step.
Common Use Cases
Homework & Exams
Show full Euclidean-algorithm working for HCF and LCM problems step by step.
Simplifying Fractions
Divide numerator and denominator by their HCF to reduce fractions fully.
Syncing Schedules
Use the LCM to find when repeating cycles — buses, shifts, orbits — next coincide.
Recipe & Batch Scaling
Find common batch sizes and evenly divisible portions with HCF and LCM.
Pro Tips
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Euclidean Shortcut
gcd(a, b) = gcd(b, a mod b) — repeat until the remainder is 0; the last divisor is the answer.
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LCM From HCF
LCM(a, b) = (a × b) ÷ HCF(a, b) — always faster than listing multiples.
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Check Coprimes
If the HCF is 1, the numbers share no factors (coprime) and the LCM is just their product.
FAQs
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