Explanation:

- The Least Common Multiple (LCM) of several numbers is the smallest multiple they all share. For 165, 176, 385, and 495, calculate their prime factorizations to find the LCM.

- The Highest Common Factor (HCF) is the largest number that divides all the given numbers without any remainder.

- For LCM divided by HCF, identify the prime factors and compute both LCM and HCF.

- The quotient of LCM divided by HCF gives the value 'p'.

To find the LCM:

- 165 = 3 x 5 x 11

- 176 = 2^4 x 11

- 385 = 5 x 7 x 11

- 495 = 3 x 5 x 11

- LCM is calculated by taking the highest power of all prime factors present in any of the numbers, so LCM = 2^4 x 3 x 5 x 7 x 11 = 55440.

For HCF:

- HCF = 11 (as it is the only common prime factor with the smallest power in all numbers).

Now calculate 'p':

- \( p = \frac{LCM}{HCF} = \frac{55440}{11} = 5040 \).

The correct option: 2- 5040

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