To determine the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of the numbers 24 and 36, it’s essential to understand their mathematical relationships. The LCM of two numbers is the smallest number that both can divide into without leaving a remainder, while the GCD is the largest number that can divide both numbers exactly. This article will explore the calculations and methods used to find these values.

Understanding the GCD of 24 and 36

The Greatest Common Divisor (GCD) of two numbers is found by determining their common factors. For 24 and 36, we first list the factors: 24 has factors 1, 2, 3, 4, 6, 8, 12, 24, and 36 has factors 1, 2, 3, 4, 6, 9, 12, 18, 36. The highest common factor is 12. Therefore, the GCD of 24 and 36 is 12.

Calculating the LCM of 24 and 36

The Least Common Multiple (LCM) is calculated using the formula: LCM = (a × b) / GCD. For 24 and 36, we use their GCD of 12 in the formula: LCM = (24 × 36) / 12. This simplifies to 72. Thus, the LCM of 24 and 36 is 72.

Applications and Importance

Knowing the LCM and GCD is useful in various applications, including fraction simplification, scheduling problems, and finding common denominators. The LCM helps in determining the smallest time interval that repeats periodically, while the GCD is essential for reducing ratios and simplifying fractions.

In summary, understanding how to find the GCD and LCM of 24 and 36 helps in solving practical mathematical problems. The GCD of 24 and 36 is 12, and the LCM is 72. These concepts are fundamental in both academic and real-world applications.