Questions: (7) LCM of 21 and 28

Solution Steps

To find the Least Common Multiple (LCM) of two numbers, we can use the relationship between the LCM and the Greatest Common Divisor (GCD). The LCM of two numbers can be calculated by dividing the product of the numbers by their GCD.

To find the LCM of \( 21 \) and \( 28 \), we first need to calculate the Greatest Common Divisor (GCD). The GCD can be found using the prime factorization method or the Euclidean algorithm. For \( 21 \) and \( 28 \):

• \( 21 = 3 \times 7 \)
• \( 28 = 2^2 \times 7 \)

The common factor is \( 7 \), so: \[ \text{GCD}(21, 28) = 7 \]

Using the relationship between LCM and GCD, we can calculate the LCM using the formula: \[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \] Substituting the values: \[ \text{LCM}(21, 28) = \frac{|21 \times 28|}{7} \] Calculating the product: \[ 21 \times 28 = 588 \] Now, substituting back: \[ \text{LCM}(21, 28) = \frac{588}{7} = 84 \]

Final Answer