Questions: What is the least common multiple of 20 and 16?

Solution Steps

To find the least common multiple (LCM) of \( 20 \) and \( 16 \), we first need to calculate the greatest common divisor (GCD) of the two numbers. The GCD can be found using the prime factorization method or the Euclidean algorithm.

Once we have the GCD, we can use the relationship between LCM and GCD, which is given by the formula: \[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \] In this case, we will substitute \( a = 20 \) and \( b = 16 \) into the formula.

Using the values of \( a \), \( b \), and the GCD obtained in Step 1, we will compute the LCM: \[ \text{LCM}(20, 16) = \frac{|20 \times 16|}{\text{GCD}(20, 16)} \] This will yield the least common multiple of \( 20 \) and \( 16 \).

Final Answer