LCM and HCF Calculator SG
Find the LCM (lowest common multiple) and HCF/GCD (highest common factor) of two or more whole numbers instantly.
How it works
Enter two or more whole numbers separated by commas. The calculator returns both the lowest common multiple (LCM) and the highest common factor (HCF, also called the GCD).
Frequently asked questions
What is the difference between LCM and HCF?
HCF is the largest number dividing both values; LCM is the smallest number both values divide into.
How do I find the HCF of two numbers?
Factor both into primes and multiply the lowest power of each shared prime. For 12 and 18, that is 2×3 = 6.
How do I find the LCM?
Take the highest power of every prime appearing in either number. For 12 and 18, that is 2²×3² = 36.
Is there a relationship between LCM and HCF?
Yes. LCM × HCF equals the product of the two numbers, so you can find one from the other.
What is HCF used for?
Simplifying fractions to lowest terms and splitting things into the largest equal groups.
What is LCM used for?
Finding common denominators for fractions and working out when repeating cycles coincide.
LCM and HCF explained
The HCF (highest common factor, also called GCD) of two numbers is the largest number that divides both exactly. The LCM (least common multiple) is the smallest number that both divide into. This calculator finds both for the numbers you enter.
Using prime factorization
Break each number into prime factors. For 12 = 2²×3 and 18 = 2×3²: the HCF takes the lowest power of each shared prime (2¹×3¹ = 6), and the LCM takes the highest power of every prime that appears (2²×3² = 36).
A useful shortcut
For any two numbers, LCM × HCF = the product of the two numbers. With 12 and 18: 36 × 6 = 216 = 12 × 18. So once you have one, you can find the other by dividing the product by it.
These ideas have practical uses: the HCF simplifies fractions to lowest terms, while the LCM gives the common denominator needed to add fractions and helps solve problems about events that repeat on different cycles.
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