Answer:
The first four prime numbers are 2, 3, 5, and 7.
Since a, b, and c are any three of these prime numbers, we can arrange them in different orders to get different values of n = a^2bc.
Here are the possible values of n:
- a = 2, b = 3, c = 5: n = 2^2 × 3 × 5 = 60
- a = 2, b = 5, c = 3: n = 2^2 × 5 × 3 = 60
- a = 3, b = 2, c = 5: n = 3^2 × 2 × 5 = 90
- a = 3, b = 5, c = 2: n = 3^2 × 5 × 2 = 90
- a = 5, b = 2, c = 3: n = 5^2 × 2 × 3 = 150
- a = 5, b = 3, c = 2: n = 5^2 × 3 × 2 = 150
The smallest value of n is 60, and the largest value is 150.
So, the smallest English value of n is sixty, and the largest English value of n is one hundred and fifty.
Answer:
MARKA AS BRAINLIST
Step-by-step explanation:
Let's determine the first four prime numbers:
\[ \text{First four prime numbers} = 2, 3, 5, 7 \]
We need to find all possible values of \( n = a^2bc \), where \( a, b, c \) are any three of these prime numbers.
Let's evaluate \( n \) for each combination of \( a, b, c \):
1. **For \( a = 2, b = 3, c = 5 \):**
\[ n = 2^2 \cdot 3 \cdot 5 = 4 \cdot 3 \cdot 5 = 60 \]
2. **For \( a = 2, b = 3, c = 7 \):**
\[ n = 2^2 \cdot 3 \cdot 7 = 4 \cdot 3 \cdot 7 = 84 \]
3. **For \( a = 2, b = 5, c = 7 \):**
\[ n = 2^2 \cdot 5 \cdot 7 = 4 \cdot 5 \cdot 7 = 140 \]
4. **For \( a = 3, b = 5, c = 7 \):**
\[ n = 3^2 \cdot 5 \cdot 7 = 9 \cdot 5 \cdot 7 = 315 \]
Among these values of \( n \), the smallest is \( 60 \).
Therefore, the smallest value of \( n \) that can be formed where \( a, b, c \) are any three of the first four prime numbers is \( \boxed{60} \).
