The smallest 2-digit composite number is 10. The divisors of 10 are 1, 2, 5, 10.The smallest composite number is 4. The divisors of 4 are 1, 2, 4.Let's find their LCM by Prime Factorization$4 = 1 \times 2 \times 2$$10 = 1 \times 2 \times 5$$LCM = 2 \times 2 \times 5 = 20$Therefore, the LCM of the smallest two-digit composite number and the smallest composite number is 20.