What is the least common multiple (LCM) of 12 and 18?

To find the least common multiple (LCM) of 12 and 18, we first look at the prime factorization of each number.

The prime factorization of 12 is:

• 12 = 2^2 * 3^1

The prime factorization of 18 is:

• 18 = 2^1 * 3^2

To determine the LCM, we take the highest power of each prime factor that appears in the factorizations.

• For the prime factor 2, the highest power between 12 and 18 is 2^2.
• For the prime factor 3, the highest power is 3^2.

Now, we multiply these together to find the LCM:

• LCM = 2^2 * 3^2 = 4 * 9 = 36.

Thus, the least common multiple of 12 and 18 is 36, which confirms why this answer is correct. The LCM is essentially the smallest number that both original numbers can divide into without leaving a remainder, and in this case, that number is 36.