Gcf And Lcm Calculator For 3 Numbers

Calculate GCF and LCM for three numbers:

\[ \text{GCF}(a,b,c) = \text{GCF}(\text{GCF}(a,b), c) \] \[ \text{LCM}(a,b,c) = \text{LCM}(\text{LCM}(a,b), c) \]

Greatest Common Factor (GCF):

Least Common Multiple (LCM):

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1. What is GCF and LCM?

The GCF (Greatest Common Factor) is the largest number that divides each of the numbers without leaving a remainder. The LCM (Least Common Multiple) is the smallest number that is a multiple of each of the numbers.

2. How Does the Calculator Work?

The calculator uses these mathematical principles:

\[ \text{GCF}(a,b,c) = \text{GCF}(\text{GCF}(a,b), c) \] \[ \text{LCM}(a,b,c) = \text{LCM}(\text{LCM}(a,b), c) \]

Where:

GCF is calculated using the Euclidean algorithm
LCM is calculated using the relationship between GCF and LCM

3. Importance of GCF and LCM

Details: GCF and LCM are fundamental concepts in number theory with applications in simplifying fractions, solving equations, scheduling problems, and cryptography.

4. Using the Calculator

Tips: Enter three positive integers. The calculator will find both the GCF and LCM of these numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between GCF and GCD?
A: They are the same concept - Greatest Common Factor (GCF) and Greatest Common Divisor (GCD) are interchangeable terms.

Q2: Can these functions handle more than three numbers?
A: Yes, the same approach can be extended to any number of integers by iteratively applying the GCF/LCM functions.

Q3: What's the relationship between GCF and LCM?
A: For two numbers a and b: GCF(a,b) × LCM(a,b) = a × b

Q4: What is the GCF/LCM if one number is 0?
A: GCF is undefined for zero, and LCM would be zero. This calculator requires positive integers.

Q5: What are some practical uses of GCF and LCM?
A: GCF is used to simplify fractions, while LCM is used to find common denominators or solve problems involving repeating cycles.