27. Find the smallest number that can be represented as the sum of five, six, and seven consecutive natural numbers.
27. The sum of five consecutive natural numbers has the form:

$$
n+(n+1)+(n+2)+(n+3)+(n+\dot{4})=5(n+2)
$$

i.e., this sum is divisible by 5. Similarly, we prove that the sum of seven consecutive natural numbers is divisible by 7, and the sum of six consecutive natural numbers has the form $3(2 n+5)$, i.e., it is an odd number divisible by 3. The smallest odd natural number that is divisible by 3, 5, and 7 is 105. Indeed, $105=19+20+$ $+21+22+23=15+16+17+18+19+20=12+13+14+15+$ $+16+17+18$