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HCF & LCM Calculator

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The HCF (GCF) and LCM calculator helps you find the highest common factor and least common multiple simultaneously. These values are often needed together, so this calculator provides both in one place. The HCF finder also shows the steps for calculating both HCF and LCM using three different methods, highlighting the common factors.

What is HCF?

HCF stands for Highest Common Factor. It is the largest factor that is common among the values under consideration. HCF and GCF are different terms for the same concept, also known as GCD (Greatest Common Divisor).

What is LCM?

LCM stands for Least Common Multiple. Unlike HCF, LCM is the smallest multiple common to the values under study.

Methods to Find HCF and LCM

There are three main methods to find the HCF or LCM for two or more numbers:

• 1. Prime Factorization
• 2. Division Method
• 3. Listing Factors/Multiples

The prime factorization method is the most commonly used. Here's an example:

Example:

Find the HCF of 16 and 32 using the prime factorization method.

Solution:

1. Break down into prime factors:

   - 16 = 2 x 2 x 2 x 2 = 2⁴

   - 32 = 2 x 2 x 2 x 2 x 2 = 2⁵

2. Identify similar factors:

   - Both numbers have 2⁴ as a common factor.

3. Multiply the common factors:

   - 2⁴ = 2 x 2 x 2 x 2 = 16

Hence, the HCF of 16 and 32 is 16.