How to use it
Type the numbers with a space between them, like 84 120. You can enter from one to eight positive whole numbers. With just one number, you get its prime factorization and find out whether it's prime.
Reading the division ladder
Each number gets its own ladder: the number and each new quotient go down the left side, and the prime you divided by goes on the right. Always try the smallest prime first (2, then 3, 5, 7…) and stop when you reach 1. The primes on the right are the prime factorization, for example \(84 = 2^2 \cdot 3 \cdot 7\).
Once you have the factorizations, the two rules are short:
- GCF (greatest common factor): use only the primes found in every number, each with its smallest exponent.
- LCM (least common multiple): use every prime that shows up at least once, each with its largest exponent.
Since \(84 = 2^2 \cdot 3 \cdot 7\) and \(120 = 2^3 \cdot 3 \cdot 5\), the shared primes are 2 and 3, so \(\text{GCF} = 2^2 \cdot 3 = 12\). For the LCM, take everything: \(2^3 \cdot 3 \cdot 5 \cdot 7 = 840\).
When you need them
The LCM is the least common denominator when you add fractions, and it answers questions like “two buses leave the station together; one runs every 12 minutes and one every 18, so when do they leave together again?” The GCF simplifies fractions and splits things into equal groups with nothing left over, such as packing 84 pencils and 120 erasers into identical kits.
For two numbers there's a built-in check: GCF × LCM equals the product of the numbers. Here \(12 \cdot 840 = 10{,}080 = 84 \cdot 120\). The tool shows this check at the end of the steps.