LCM & GCF (HCF) Calculator

The LCM & GCF (HCF) calculator helps you find the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) and the Least Common Multiple (LCM) for a set of integers. GCD/HCF is the largest factor that divides every number in the set without remainder, while LCM is the smallest positive multiple divisible by all numbers in the set.

We use the Euclidean Algorithm to compute the GCD efficiently and show each step (for example, repeating a = b × q + r until the remainder is 0). For the LCM, we apply the standard formula LCM(a, b) = |a·b| / GCD(a, b) and extend it to multiple numbers pairwise, making the final result transparent.

Topics covered include: definitions and properties of GCD/HCF, LCM via GCD, handling special cases such as zero, and the Euclid step notation commonly used in math textbooks. This is useful for fraction simplification, periodic scheduling, modular arithmetic, number theory, and many computational applications.

• If the set has only one number, the GCD is the absolute value of that number.
• If one number is 0, the GCD is defined by the other number; the LCM of a set containing 0 is 0.
• For (0, 0) we define GCD = 0 for operational clarity.
• The tool accepts comma- or space-separated input and requires integers.

Example uses: simplifying fractions (divide numerator and denominator by the GCD), finding common meeting periods for repeated schedules (using the LCM), or analyzing common factors in integer datasets. With detailed Euclidean steps, this calculator is ideal for self-study and classroom support.