$ \mathrm{GCD}(48, 72) = 24 $, so $ \mathrm{LCM}(48, 72) = \frac{48 \cdot 72}{24} = 48 \cdot 3 = 144 $.

["Understanding GCD and LCM: Why GCD(48, 72) = 24 and LCM(48, 72) = 144", "When learning about number theory, one of the key concepts is the relationship between the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of two integers. A classic example that brings this relationship to life is calculating LCM using the formula:", "$$\n\mathrm{LCM}(a, b) = \frac{a \cdot b}{\mathrm{GCD}(a, b)}\n$$", "Take the numbers 48 and 72:\nWe first find\n$$\n\mathrm{GCD}(48, 72) = 24\n$$\nUsing the formula:\n$$\n\mathrm{LCM}(48, 72) = \frac{48 \cdot 72}{24}\n$$\nSimplify it step-by-step:\n$$\n48 \cdot 72 = 3456, \quad \frac{3456}{24} = 144\n$$\nSo,\n$$\n\mathrm{LCM}(48, 72) = 144\n$$", "This elegant connection shows that understanding GCD directly unlocks efficient computation of LCM.\nWhy is GCD(48, 72) = 24?\nThe GCD represents the largest number dividing both 48 and 72. Factoring both:", "- $48 = 2^4 \cdot 3$\n- $72 = 2^3 \cdot 3^2$\nThe GCD takes the lowest powers of common primes:\n$$\n\mathrm{GCD} = 2^3 \cdot 3 = 8 \cdot 3 = 24\n$$", "Now, since the product $48 \cdot 72 = 3456$, dividing by GCD gives:\n$$\n\mathrm{LCM} = \frac{3456}{24} = 144\n$$", "In summary:\n- The GCD of 48 and 72 is 24.\n- Using LCM formula, $ \mathrm{LCM}(48, 72) = \frac{48 \cdot 72}{24} = 144 $.\n- This illustrates how GCD enables fast LCM computation and highlights deep number relationships used in math, programming, and real-world applications like scheduling and grouping.", "Mastering GCD and LCM not only helps in mathematics but also boosts problem-solving precision in science, computer science, and everyday planning."]