\text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72

Sun, 03 May 2026 04:09:08 +0000

# Understanding LCM: Why 2³ × 3² Equals 72 — The Key to Finding the Least Common Multiple When diving into math fundamentals, one concept that often puzzles learners is the Least Common Multiple (LCM). Whether in homework, exams, or real-world applications, understanding LCM is essential for working with fractions, scheduling, ratios, and more. One classic example to clarify this concept is calculating LCM using prime factorization: €LCM = 2³ × 3² = 8 × 9 = 72. In this article, we’ll break down exactly why this formula works, walk through the math step-by-step, and explore how the LCM connects to everyday math problems. ## What Is the Least Common Multiple (LCM)? The Least Common Multiple of two or more integers is the smallest positive number that all given numbers divide without leaving a remainder. It’s a crucial value in fraction addition, number theory, and periodic events. Unlike the Greatest Common Divisor (GCD), which finds the largest shared factor, LCM identifies the smallest shared multiple—making it especially useful for alignment of cycles or sharing resources evenly.