Final answer:
The LCM of 40 and 72 is found by prime factorization: 40 is 2^3 x 5, and 72 is 2^3 x 3^2. Taking the highest powers of these prime factors, the LCM is 2^3 x 3^2 x 5, which calculates to 360.
Step-by-step explanation:
The Least Common Multiple (LCM) of two numbers can be found by using the method of prime factorization. Let's apply this method to find the LCM of 40 and 72.
First, we prime factorize each number:
40 = 23 × 5
72 = 23 × 32
Then, we take the highest powers of all the prime factors. This gives us:
23 (since 23 is the highest power of 2 that appears)
32 (since 32 is the highest power of 3 that appears)
5 (the factor of 5 appears in the prime factorization of 40 but not in 72, so we take 51)
The LCM is therefore:
LCM = 23 × 32 × 5 = 8 × 9 × 5 = 360
So, the LCM of 40 and 72 is 360.