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Advanced ⛓ Discrete Math & Number Theory Topic 72 of 103

GCD and LCM

Greatest common divisor and least common multiple.

Key idea

Greatest common divisor and least common multiple.

In depth

gcd(a, b) is the largest common divisor and lcm(a, b) the smallest common multiple, with gcd(a, b) × lcm(a, b) = ab. Using prime factorisations, gcd takes minimum exponents, lcm maximum.

Worked example

gcd(12, 18) = 6, lcm = 36, and 6 × 36 = 216 = 12 × 18.

Formula

gcd·lcm = ab

Real-world uses

Common mistake

Applying gcd × lcm = ab to three or more numbers.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is GCD and LCM?

Greatest common divisor and least common multiple. It is a topic at the advanced level in Discrete Math & Number Theory.

What is the formula for GCD and LCM?

The key formula is gcd·lcm = ab.

Where is GCD and LCM used in real life?

Real-world examples: Simplifying fractions and scheduling events that repeat at different intervals.

What should I learn before GCD and LCM?

Make sure you are comfortable with Prime Number Theorem, the previous topic in Discrete Math & Number Theory.

What is a common mistake with GCD and LCM?

Applying gcd × lcm = ab to three or more numbers.

How can I practise GCD and LCM?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after GCD and LCM?

Move on to Extended Euclidean Algorithm next.

Related advanced topics in Discrete Math & Number Theory