This calculator finds the least common multiple of two numbers. The code behind the lcm calculator is based on the prime factorization method; we factor the two numbers to get prime factor candidates, combine them for the two numbers, and multiply them together. The result is the lowest common multiple.
We have a second calculator on this site which can be used to find the greatest common factor of two numbers. (also known as the greatest common divisor) The gcf calculator generates an integer result and is useful for algebra problems. We have other math solver tools as well.
The typical approach to calculating a lcm is to use the prime factorization method. You can do this via pen & paper (assuming you don't want to just use our LCM calculator - to check your work, of course). Each of the two numbers is factored down to a set of unique prime numbers. These two sets are combined, eliminating common items and preserving the highest exponent. The remaining numbers are multiplied together to get the smallest multiple of the numbers. The result is the smallest common multiple.
To perform a LCM calculation via this online calculator, enter the two numbers and hit the calculate button.
The Euclidean Algorithm is an efficient way of computing the GCD of two integers. It was discovered by the Greek mathematician Euclid, who determined that if n goes into x and y, it must go into x-y. Therefore, we can subtract the smaller number from the larger number until the remainder is less than the smaller number. We continue using this process until the remainder is 0, thus leaving us with our GCD. This is part of our GCD calculator.