GCF and LCM Calculator (HCF and LCM)

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Updated October 27, 2026

The greatest common factor is the largest number that divides two numbers exactly, and the least common multiple is the smallest number both divide into. They are used to simplify fractions and add them. This free GCF and LCM calculator solves for whichever value you leave blank and shows the formula and steps.

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Type in any field to change it. Press × on a value to calculate that field instead.

How to use the GCF and LCM calculator

Enter two whole numbers. The calculator shows their greatest common factor (GCF, also called HCF or GCD) and least common multiple (LCM).

The Euclidean algorithm

The fastest way to find the GCF is to repeatedly replace the larger number with the remainder of dividing it by the smaller one:

Step Division Remainder
1 84 ÷ 36 = 2 12
2 36 ÷ 12 = 3 0

When the remainder reaches 0, the last non-zero remainder — 12 — is the GCF.

Then LCM = 84 × 36 ÷ 12 = 252.

Prime factorisation method

Write each number as a product of primes:

  • 84 = 2² × 3 × 7

  • 36 = 2² × 3²

  • GCF: lowest power of each common prime — 2² × 3 = 12

  • LCM: highest power of every prime — 2² × 3² × 7 = 252

GCF and LCM table

Numbers GCF LCM
12, 18 6 36
15, 25 5 75
24, 36 12 72
8, 12 4 24
14, 21 7 42
45, 60 15 180
17, 23 1 391
100, 75 25 300

Numbers with a GCF of 1, such as 17 and 23, are coprime.

Where they are used

  • Simplifying fractions: divide top and bottom by the GCF. 36/84 = 3/7.
  • Adding fractions: use the LCM of the denominators as the common denominator. 1/12 + 1/18 uses 36.
  • Scheduling: two buses every 12 and 18 minutes leave together every 36 minutes (the LCM).
  • Tiling: the largest square tile that fits a 84 × 36 cm area exactly is 12 cm (the GCF).

Frequently asked questions

What is the GCF of 84 and 36?

12. The LCM is 252.

What is the difference between HCF and GCF?

Nothing — highest common factor (HCF), greatest common factor (GCF) and greatest common divisor (GCD) all mean the same thing.

How are GCF and LCM related?

For two positive whole numbers, GCF × LCM = a × b. So LCM = a × b ÷ GCF.

How do I find the GCF of three numbers?

Find the GCF of the first two, then the GCF of that result and the third number. The LCM works the same way.

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