Find the least common multiple (LCM) of the numbers 12, 15, and 20.

The correct answer is 60.

To find the Least Common Multiple (LCM) of 12, 15, and 20, we can use the prime factorization method.

Step 1: Find the prime factorization of each number.

$12=2^2\times 3$

$15=3\times 5$

$20=2^2\times 5$

Step 2: Find the highest power of each prime factor involved.

The prime factors present in the numbers are 2, 3, and 5.

Highest power of prime factor 2: $2^2$

Highest power of prime factor 3: $3^1$

Highest power of prime factor 5: $5^1$

Step 3: Multiply the highest powers of these prime factors to find the LCM.

$\text{LCM}(12,15,20)=2^2\times 3\times 5$

$\text{LCM}(12,15,20)=4\times 3\times 5=60$

Thus, the least common multiple (LCM) of 12, 15, and 20 is 60.