(LCM of 96, 120 and 160) ÷ (HCF of 72 and 168) is equal to

The correct option is 20.

To find the value of the expression, we need to calculate the Least Common Multiple (LCM) of 96, 120, and 160, and divide it by the Highest Common Factor (HCF) of 72 and 168.

Step 1: Find the LCM of 96, 120, and 160
Let us find the prime factorization of each number:
$96=2^5\times 3$
$120=2^3\times 3\times 5$
$160=2^5\times 5$

To find the LCM, we take the highest power of each prime factor that appears in these factorizations:
- For prime factor 2, the highest power is $2^5$.
- For prime factor 3, the highest power is $3^1$.
- For prime factor 5, the highest power is $5^1$.

Therefore, the LCM is:
$\text{LCM}(96,120,160)=2^5\times 3\times 5=32\times 15=480$

Step 2: Find the HCF of 72 and 168
Let us find the prime factorization of these two numbers:
$72=2^3\times 3^2$
$168=2^3\times 3\times 7$

To find the HCF, we take the lowest power of the common prime factors:
- For prime factor 2, the lowest power is $2^3$.
- For prime factor 3, the lowest power is $3^1$.
- Prime factor 7 is not common to both.

Therefore, the HCF is:
$\text{HCF}(72,168)=2^3\times 3=8\times 3=24$

Step 3: Calculate the final value
Now we substitute the values into the given expression:
$\frac{\text{LCM of 96, 120 and 160}}{\text{HCF of 72 and 168}}=\frac{480}{24}=20$