What is the greatest common factor?

The greatest common factor, or GCF, is the largest whole number that divides into all the numbers with no remainder. For 12 and 18 it is 6. It is used to simplify fractions and ratios.

What is the lowest common multiple?

The lowest common multiple, or LCM, is the smallest number that all the numbers divide into. For 4 and 6 it is 12. It is used to add fractions with different denominators.

How are GCF and LCM related?

For two numbers, the GCF times the LCM equals the product of the two numbers. So once you know one, you can find the other. The calculator works out both directly for any list.

GCF and LCM Calculator

This calculator works out the greatest common factor (GCF) and the lowest common multiple (LCM) of two or more whole numbers in one step, saving you long division or trial and error when you need both figures for schoolwork, everyday maths or programming. Type your numbers into the single input field, separated by commas or spaces, and the calculator recalculates instantly as you type. It returns the greatest common factor, the largest whole number that divides every number you entered with nothing left over, and the lowest common multiple, the smallest whole number that every one of your numbers divides into exactly. Behind the scenes it applies the Euclidean algorithm to find the GCF efficiently, then uses the relationship between GCF and LCM to work out the second figure without a lengthy search through multiples. Because it works with any number of values, not just pairs, you can check three, four or more numbers at once, handy when adding several fractions with different denominators or simplifying a ratio to its lowest terms. Use the GCF to reduce a fraction or ratio to its simplest form, and the LCM to find a common denominator when adding or comparing fractions. Below the calculator, a worked example and a short explanation of the method walk through exactly how each result is reached.

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Numbers

Greatest common factor0

Lowest common multiple0

How it works

The calculator uses the Euclidean algorithm to find the GCF of the numbers, taking remainders until one divides the other exactly. The LCM is then found from the rule that, for each pair, the GCF times the LCM equals the product, applied across the whole list.

Worked example

For 12, 18, and 24, the greatest common factor is 6, the largest number dividing all three. The lowest common multiple is 72, the smallest number all three divide into.

Related calculators

Fraction Calculator: add and simplify fractions.
Ratio Calculator: simplify ratios.
Square Root Calculator: roots of a number.
Factorial Calculator: n factorial.

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