Find the LCM of 40 and 90.

To find the LCM (least common multiple) of 40 and 90, we can use the prime factorization method as follows:

Step 1: Find the prime factorization of each number:

• 40 = 2^3 x 5
• 90 = 2 x 3^2 x 5

Step 2: Identify the common prime factors and their highest powers:

• The common prime factors are 2 and 5.
• The highest power of 2 is 3 (from 40).
• The highest power of 3 is 2 (from 90).
• The highest power of 5 is 1 (from 40).

Step 3: Multiply the common prime factors by their highest powers:

2^3 x 3^2 x 5^1 = 360

Therefore, the LCM of 40 and 90 is 360.