LCM calculator
For any two numbers, LCM × GCD equals their product. With 4 and 6 that is 12 × 2 = 24. Seeing the pair together is the quickest way to sanity-check either one, and the GCD is what you need to reduce a fraction.
The lowest common multiple of a set of whole numbers is the smallest number that every one of them divides into exactly. For 4, 6 and 10 it is 60. The greatest common divisor is the largest number that divides into all of them, which here is 2. Both are computed with Euclid’s algorithm, applied pairwise across the list.
How to use it
The everyday use is adding fractions. To add 1/4 and 1/6 you need a common denominator, and the lowest common multiple of 4 and 6 — twelve — is the smallest one that works. Using the product, 24, also works but leaves you reducing afterwards.
Questions
Yes. Highest common factor and greatest common divisor are two names for the same thing; British and American textbooks differ.