GCD & LCM Calculator

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Deep Dive: GCD and LCM

What is Greatest Common Divisor?

The **GCD** (also known as Highest Common Factor - HCF) of two or more integers is the largest positive integer that divides each of the integers without a remainder.

For example, the GCD of 8 and 12 is 4, because it's the largest number that divides both.

What is Least Common Multiple?

The **LCM** of two or more integers is the smallest positive integer that is divisible by all the numbers in the set.

For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 can divide into.

Methods Used

Euclidean Algorithm: An efficient method for computing the GCD by repeatedly replacing the larger number with the remainder of the division.
LCM Property: We use the formula LCM(a,b) = |a*b| / GCD(a,b) to find the multiple quickly.

Frequently Asked Questions

The GCD of 0 and any number *n* is |n|. However, GCD(0,0) is mathematically undefined.

Coprime numbers (or relatively prime) are two numbers whose Greatest Common Divisor is 1. Example: 8 and 9.

Real-world Use

GCD is essential for simplifying fractions and solving tiling problems. LCM is used for scheduling events that happen at different intervals.

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