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LCM and GCF Calculator

Calculate the Least Common Multiple (LCM) and Greatest Common Factor (GCF/GCD) for up to 6 numbers. Shows prime factorisation and step-by-step working.

Enter Numbers
Numbers (up to 6)
A
B
C
D
E
F
Your Result

Fill in the details and
your result appears here.

LCM
LCM (Least Common Multiple)
GCF / GCD
Prime Factorisation
LCM ÷ GCF
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Did You Know?
Fraction trick using LCM
To add 1/12 + 1/18: find LCM(12,18)=36. Convert: 3/36 + 2/36 = 5/36. LCM gives you the lowest common denominator, keeping numbers small and calculation clean.

How to use this calculator

1

Enter 2 to 6 numbers

At least A and B are required. C through F are optional.

2

Read LCM and GCF

LCM is the smallest number divisible by all inputs. GCF is the largest factor shared by all inputs.

3

Check prime factorisation

See how each number breaks into prime factors — useful for understanding the result.

The formula explained

GCF(a,b) = largest number dividing both a and b evenly
LCM(a,b) = a × b ÷ GCF(a,b)

The Euclidean algorithm finds GCF efficiently: repeatedly replace the larger number with the remainder when divided by the smaller. When remainder is 0, the last non-zero value is the GCF.

Frequently Asked Questions

What is LCM used for?

Adding fractions with different denominators (find LCM of denominators). Scheduling problems (when will two events coincide again). Gear ratios, music rhythm calculations.

What is GCF used for?

Simplifying fractions (divide by GCF of numerator and denominator). Splitting things into equal groups. Finding the largest tile size that fits a floor without cutting.

What is the difference between GCF and GCD?

They are the same thing. GCF = Greatest Common Factor. GCD = Greatest Common Divisor. Different textbooks use different terms for identical concepts.

LCM of 12 and 18?

GCF(12,18) = 6. LCM = 12×18÷6 = 36. Verify: 36÷12=3 (whole), 36÷18=2 (whole). 36 is the smallest number divisible by both 12 and 18.

What is the GCF of 12 and 18?

GCF of 12 and 18: factors of 12 are 1,2,3,4,6,12 and factors of 18 are 1,2,3,6,9,18. The largest common factor is 6.

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