What is the LCM of 12 and 30?

To find the least common multiple (LCM) of 12 and 30, we can use the prime factorization method.

First, we need the prime factorization of each number:

• 12 can be factored into 2 × 2 × 3, or in prime factorization form, it’s 2² × 3¹.
• 30 can be factored into 2 × 3 × 5, or in prime factorization form, it’s 2¹ × 3¹ × 5¹.

Next, we take the highest power of each prime that appears in either factorization:

• The highest power of 2 is 2².
• The highest power of 3 is 3¹.
• The highest power of 5 is 5¹.

Now, we multiply these together:

LCM = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60.

Therefore, the LCM of 12 and 30 is 60.