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Arithmetic

LCM and GCF

Formula
LCM(a, b) = (a × b) / GCF(a, b)

What is LCM and GCF?

The Least Common Multiple (LCM) is the smallest number that both numbers divide into evenly. The Greatest Common Factor (GCF) is the largest number that divides both evenly. They are related by the formula LCM × GCF = a × b.

Variables

  • L
    LCM — Least Common Multiple
  • G
    GCF — Greatest Common Factor
  • a
    a, b — Two positive integers

Worked Examples

Example 1

Find the LCM of 12 and 18.

Solution:

GCF(12, 18) = 6. LCM = (12 × 18) / 6 = 216 / 6 = 36

Frequently Asked Questions

Related Formulas

Percentage Change

((New Value − Original Value) / Original Value) × 100

Simple Interest

I = (P × R × T) / 100

Compound Interest

A = P × (1 + R/100)^T

Speed, Distance, Time

Speed = Distance / Time

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