The smallest two-digit composite number is 10 (which is not prime because it can be divided by 1, 2, 5, and 10), and the smallest composite number is 4 (as it can be divided by 1, 2, and 4).
To calculate the least common multiple (LCM) of these two numbers, we need to find the multiples of each number:
- Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100…
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60…
From this list, we see that both numbers share common multiples. To find the smallest common multiple, we look for the first number that appears in both lists. Both lists show that the first common multiple is 20.
We can also confirm this by using the prime factorization method:
- Prime factorization of 10: 2 x 5
- Prime factorization of 4: 2 x 2
To find the LCM, we take the highest power of all prime factors involved:
- Highest power of 2 is 2^2 (from 4)
- Highest power of 5 is 5^1 (from 10)
Therefore, the LCM is calculated as:
LCM = 2^2 x 5^1 = 4 x 5 = 20
Thus, the least common multiple of the smallest two-digit composite number (10) and the smallest composite number (4) is 20.