The least common multiple (LCM) of 12 and 24 is 24. To find the LCM, we can use the method of prime factorization or list the multiples of each number.
First, let’s look at the multiples of 12: 12, 24, 36, 48, 60, …
Now, let’s look at the multiples of 24: 24, 48, 72, …
The smallest multiple that appears in both lists is 24. Therefore, the LCM of 12 and 24 is 24.
Another way to confirm this is by using the prime factorization method:
12 can be expressed as: 2² × 3
24 can be expressed as: 2³ × 3
To find the LCM, we take the highest power of each prime: 2³ (from 24) and 3¹ (from both). Thus, the LCM is:
LCM = 2³ × 3¹ = 8 × 3 = 24
In conclusion, whether you list the multiples or use prime factorization, you’ll find that the least common multiple of 12 and 24 is 24.