LCM and GCF Calculator (Also Finds the LCD)

This LCM and GCF calculator finds the least common multiple and the greatest common factor of two to six whole numbers, and shows the prime factors behind both. Switch to fractions and it finds the least common denominator, or LCD, and the equivalent fractions.

The LCM is the smallest number that every input divides into. The GCF, also called the greatest common divisor, is the largest number that divides every input.

How the LCM, GCF and LCD are found

Prime factorization

Write each number as a product of primes. For the GCF, multiply the primes the numbers share, each to its lowest power. For the LCM, multiply every prime that appears, each to its highest power.

The shortcut for two numbers

For two numbers, the GCF times the LCM equals their product.

GCF × LCM = a × b

The least common denominator

The LCD of fractions is the LCM of their denominators. Rewrite each fraction with that denominator to add, subtract or compare them.

Worked examples

Example 1: three numbers

Find the LCM and GCF of 12, 18 and 30. The prime factors are 12 = 2² × 3, 18 = 2 × 3² and 30 = 2 × 3 × 5.

GCF = 2 × 3 = 6 and LCM = 2² × 3² × 5 = 180

Example 2: two numbers

For 8 and 12, the GCF is 4 and the LCM is 24. Check: 4 × 24 = 96 = 8 × 12.

Example 3: the LCD of fractions

Find the LCD of 1/4, 5/6 and 3/8. The LCM of 4, 6 and 8 is 24, so the LCD is 24.

1/4 = 6/24, 5/6 = 20/24, 3/8 = 9/24

Their sum is 6/24 + 20/24 + 9/24 = 35/24.

Frequently asked questions