Find the least common multiple of 10 and 12.

To find the least common multiple (LCM) of 10 and 12, we can use a few different methods. Here, we'll use the prime factorization method and the listing multiples method.

Prime Factorization Method

First, we break down each number into its prime factors:

• 10: 2 × 5
• 12: 2 × 2 × 3 (or 2² × 3)

Next, we take the highest power of each prime factor:

• 2 (highest power is 2²)
• 3 (highest power is 3¹)
• 5 (highest power is 5¹)

Now, we multiply these together:

LCM = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60

Listing Multiples Method

Alternatively, we can list the multiples of each number:

• Multiples of 10: 10, 20, 30, 40, 50, 60, ...
• Multiples of 12: 12, 24, 36, 48, 60, ...

The smallest common multiple in both lists is 60.

Final Result

Thus, the least common multiple of 10 and 12 is 60.