To find the least common multiple (LCM) of the smallest composite number and the smallest prime number, we first need to identify these numbers.
The smallest prime number is 2, which is only divisible by itself and 1. On the other hand, the smallest composite number is 4, as it has divisors other than 1 and itself (in this case, 2).
Next, to find the LCM of 2 and 4, we can use a couple of methods. One simple way is to list the multiples of each number:
- Multiples of 2: 2, 4, 6, 8, 10, …
- Multiples of 4: 4, 8, 12, 16, …
From the lists above, we can see that the smallest common multiple is 4.
Another method to find the LCM is to use the formula:
LCM(a, b) = (a * b) / GCD(a, b)
Here, GCD represents the greatest common divisor. For our numbers:
1. The GCD of 2 and 4 is 2.
2. Plugging into the formula gives us:
LCM(2, 4) = (2 * 4) / 2 = 4.
So, the least common multiple of the smallest composite number (4) and the smallest prime number (2) is 4.
This means that 4 is the smallest number that is evenly divisible by both 2 and 4. In conclusion, the LCM of 2 and 4 is 4.